Welcome Aboard !

Some thoughts and comments (in no particular order)....

• There are 2 screws: Idle Mixture and Idle Speed. Idle Mixture starts at 1 to 1.5 turns out, and is adjusted for maximum idle speed once idle can be set. Idle speed is adjusted per the requirements of the engine. Lots of times I simply turn the mixture screw out 1 turn and leave it. It's not important until everything else is perfect.
• Idle Mixture does not makes things lean or rich, the mixture is already set. What that screw adjusts is volume of idle mixture. Big difference.
• Idle mixture depends upon the cleanliness condition of the slow speed jet. You had the float bowl apart, what was this jet's condition?
• It sounds as if you have not taken the tops off the carbs yet. That is mandatory on a new-to-you bike if this age. The original diaphragms were not Ethanol proof and may (most probably) have rips and holes. Things to check.... 
  • Condition of diaphragm
  • Condition of carb needles (If you see anything other than bright brass then they get replaced along with the needle jet.)
  • Exposed length of carb needles. Are the lengths equal ???
• If your bike starts easily without the choke, then your mixture is way too rich. This could something as simple as a dirty air filter. Replace it. You checked the float level. You have not checked needle position. Another popular cause is reversing the choke plate from the RH carb into the LH carb. This is why I advise to only disassemble one carb at a time, but someone may have done otherwise. There are many "RH only" parts in the Bing that LOOK exactly like the LH part. 
• "Shorting method" of carb sync is totally wasted time. Build your own manometer, or buy an electronic unit and do it correctly. Here's instructions on a quick and easy sync tool for a twin..... http://www.powerchutes.com/manometer.asp
• Generally, carb adjustments are the last thing done during a Complete Tuneup. You've got a good start but there's still more. You'll need new Metal Core plug wires and new 5K Ohm plug caps. Wires and plug caps break down and cause tiny issues that are hard to locate. Since everything is under $20 it's not worth testing, just replace it if you don't know the exact age.
• There is also a enrichener jet in the bottom of the float bowl. Is that clear ??
• The fuel tanks were originally coated with a anti-rust treatment, which on many bikes of this era is now flaking off and entering the fuel system... resulting in leaking carbs. Therefore tiny fuel filters are now mandatory on both sides.
• Carb adjustments shouldn't be attempted until any bike is fully warmed. On an Airhead that takes about 10 miles. So a 2 minute run the garage is not nearly enough.
• Your biggest battle is Ethanol in the common gasoline. It runs great and I cannot suggest Ethanol-free or Avgas as an economical replacement. You need to be running "High Test" gasoline and it is HIGHLY suggested you buy a brand with built-in cleaners, like Shell or Chevron. And never, ever leave fuel in the system (tank, hoses, carb) during winter storage. 
• You'd do well to study up on Top Tier Fuels.... https://toptiergas.com/

There's a lot more, but this will keep you busy (and out of the pool halls) for a couple of weeks. From what you told us, I believe this bike has not been on the road in a LONG time. Your goal should be to be able to put several 300 mile days on using Top Tier Fuel. IME, that does as much as the tuning as far as getting an Airhead to perform up to expectations.

Hope this helps.

PS....

The correct spark plug for this bike is NGK BP7ES.

1. Pay no attention to the NGK plug chart. It is wrong.
2. NGK will soon stop making this plug, so you may want to buy 4, 6 or 8 as spares NOW.

?

@wobbly 

Thanks, Richard.  To clarify, I've done the following since purchase starting at the fuel tank, which looks clean with intact original red paint inside and no rust.  I try to only use Chevron Super in old engines, as it seemed to make my Corvair Greenbrier run better than anything else.  I'd only use something else if I was traveling and couldn't find a Chevron.  In LA, they should all be TopTier.

1. New screens on both petcocks.  Old ones came out clean, but used new anyhow

2. New BMW fuel line

3. New inline fuel filters on both sides

4. New air filter

5. New 1k ohm plug wires and Beru caps.  It is my understanding that the 1k ohm wires were OEM, but I'd have to go 5k ohm if I install any kind of electronic ignition

6. New Bosch W6DC plugs

7. New diaphrams, carefully paying attention to alignment on installation.

8. New needles.  The old ones didn't look too bad, but replaced anyhow.  Jet doesn't look worn or out of round.

9. Needles at 3rd position

10.  Full carb rebuild kit of all o-rings and new bowl and enricher gaskets, including the hidden o-ring at the end of the butterfly shaft.  Used a whole can of carb cleaner making sure all passages were clear.  Let the jets all soak for a bit before going at them with an old toothbrush. Everything was very clean to begin with, but o-rings were brittle and worn.  Bowls were shiny with no crud  and have remained that way.  Could see clearly through all jets before putting them back in.

11.  New floats, float pin, and float needle.  Needle seat appears clean.  

12.  Floats set to even with carb base when held upside down at 45 degrees.  This fills the bowls to 1/2" from edge

13.  New throttle return springs

14.  New points and condenser.  Points gapped with Northwoods tool.

16.  New battery

15.  Not that it has any bearing here, but I put new tires and a set of Ikons on it, too.  😉

The thing that is confusing to me is the left air screw.  The Bing manual says to start with it out .75 turns.  Am I wrong in thinking that screwing it in is cutting fuel?  So, with it screwed all the way in, shouldn't that carb be getting nothing?  On the right side of my bike, if you screw the air screw in from .75, it sounds like it is starving that side and lowers the idle.  If you screw it out from .75 it raises the idle until it sounds like it's flooding, at which point idle goes down again.  That seems to me to be proper behavior.  On the left side, the bike runs pretty good with the mixture screw at .75, but the idle goes up as it is screwed in.  That seems backward to me.  You can also screw it all the way in and it will hold that high idle.  I am definitely talking air/mixture screw here.  When reassembling, I set the idle screws to one turn past when they just hit the stops on the throttle.  

So it is the different behavior between the sides that is confusing.  Also what I'm seeing on the left carb does not follow normal behavior according to any of the sources I've read.  I have searched around but haven't found anyone having exactly this problem. 

Thoughts and suggestions....

• New air filter from where ?
• If the bike has over 50K miles then you need new needle jets, regardless of what you can see.
• New points, but how did you time the bike ? You need to use a strobe at Full Advance.
• Did you replace the auto advance springs ? Did you service the auto advance?
• Screwing in the Mixture screw reduces the volume of air/fuel going through the idle track. But that is not the only way the engine can get fuel. 
• And you're sure the needles are protruding from the slide the same amount on both sides?
• I do believe the OEM plug wires were metal core. 1974 pre-dates the use of resistance plug wires, and they may not have even been invented then. Check your sources.
• It doesn't matter the brand of plug cap, tell me the internal resistance.
• I'd set the Mixture screw at 1 turn and start looking elsewhere. Start with an accurate carb balancing at idle AND 1800 RPM using a liquid or electronic manometer.
• A compression test with the carbs removed would help. Run the starter until the pressure stops climbing. 
• I am still not convinced the enricheners are assembled correctly. 

Hope this helps.

When working on carbs I find it really helps to get into the correct "mindset" or understanding. These thoughts might help...

► The carb is part of a larger "system" with multiple factors affecting basic functions like "engine idle". Let's not get lost worrying about why a single screw does this or that, when idle is affected by 10 other equally important components and adjustments. This is why I suggest setting the Mixture Screws to 1 turn out, and then moving forward. 

► The carb is at the "top of the food chain" and carb performance rests on an entire foundation of non-carburetor adjustments like timing, compression, plug wire specs, etc. Most carb functions are measured by "the engine sounds right", while all the foundational pieces of the system have exact metrics that can (and must be) carefully measured. "Sounding right" is simply the end result of having all the supporting ~20 pieces of the puzzle being exactly correct. Not "thinking they look good", but rather "knowing they are correct".

► The modern instrument we know as the carb is extremely deceptive in its appearance. In my 50 years of repairing motorcycle carbs, hundreds of them brought in by customers, the primary fault I find is lack of precision during assembly. There is always evidence of new parts being lavished on the carb, but then a complete disregard for the finesse of the instrument. In my mind, the only difference between working on carbs and working on wrist watches is the carb parts are slightly larger. The same care and absolute attention to detail is mandatory. 

Hope these ideas help. All the best !

It’s too long ago to remember the details, but when chasing a problem once, I was suspecting that the engine might be drawing fuel through the enrichment circuit (choke) even when the choke was closed. I found that I could, as an experiment, push a small plastic cap over the end of the pickup tube for the enrichment circuit, that extends down into the corner of the fuel bowl. This completely eliminated any possibility of drawing fuel through that circuit. 

I’m with Richard so far as suspecting the enrichment circuit/choke valve as a problem.