Update:
I finished absolutely thoroughly and completely going through the carbs (for a 3rd or 4th time... I've lost count). Fired it up (with choke) and after letting it warm for a few minutes, I begin to slowly reduce the choke...RPMS started to fall, so I increased the Idle set screw. I blipped the throttle, and RPMS immediately dropped almost to the point of stalling (as usual). Tried a few more times, same result. I switched it off, and decreed "I give up."

On a whim, I restarted it a minute later, and let it run a while longer. Suddenly, the RPMs slowly began to pick up (like it was finally following where the Idle set screw was set.) With choke off, I dialed the set screw back down so it was around 1200 or so idle... and then dared to blip the throttle again. It revved higher than it has in 15+ years! Throttle seemed to be responding as normal. WTH? What changed from running it just a few minutes earlier?

It does seem to cycle... after a couple minutes, RPMS began to fall again requiring throttle to keep it running, but it does pick back up (with a slightly rough feel, like it's dropping a cylinder). After a minute it clears up and runs/idles smoothly. A couple minutes later it does the same thing. Also, the exhaust is a bit smokey. I'm going to resync the carbs, and, if feeling brave, take it out and see what happens. Perhaps it just needs to be 'cleared out'(?)

Fingers crossed....

 

Well you are making progress so that is encouraging. One thing to pay attention to are the carb boots. They can give you fits. If they are cracked or not 100% tight they will give you erratic results.

 

Update #2:
I ran it a few more times. After it's warm, it is *very* difficult to start. Won't even fire until many cycles of 10+ seconds of cranking. I can see the clear aux fuel tank line is full of fuel. After about a 30 minute cool down (enough time to reinstall the instruments (replace lamps with LEDs), and reinstall the tank, I could not get it to start. Pulled a plug and it's pretty black (not soaking wet though). Verified good spark. When it does run, exhaust is a bit smokey.

So seems like idle circuit is rich (or very rich). Mixture screws set at 2 3/4 turns out (factory). Puzzled as to why it would be rich (if that is the case) with factory setting. I assume next step would be to try fewer turns on the mixture screws?

I knew a ride was wishful thinking....

 

Thanks... I've replaced those after a few wrestling matches (which I lost several times) trying to get the carb stack off the intakes. The original boots had hardened quite a bit.

A couple suggestions for those contemplating removing the carbs for the first time in a while... order new boots (called insulators in the Honda parts list). Makes the carbs 1000% easier to remove and replace. Also, get Honda OEM ones. I initially got the $20 for 4 ebay special...and the inner bore is not only a little asymmetrical, it's smaller in places and doesn't match the inner diameter of the carb bores very well.) The OEM boots perfectly match the I.D. of the carb's bores (making for what I am sure is less turbulent air flow through the boot.)

 

Morning matey got up to watch the World Super Bike racing ,its 3.30 here in blighty, see you have had an improvement , your getting there, running rich though, could be float heights are they correct, not sure if the 95 were adjustable though

 

Morning! 3:30!? That's dedication.

Well, lest you think I'm on the home stretch...
Had dinner, and went back out to the garage to install the nipples in the intake vacuum ports so I could do another carb sync tomorrow. Took the bolt out of the vacuum port for Cyl #1... fuel poured out. Not a little... a LOT. And it keep going. I thought, how could that be, unless... Yep.. the ENTIRE intake track (intake valves up to the carb barrel) was full of fuel. I checked the others... Cyl #3 and #4, same. (Talk about being a little rich!)

So somehow fuel continued to flow (yes, I left the tank petcock on) from the tank..passing through the (inactive) fuel pump and filled the intakes. First thought was stuck floats (floats not adjustable), but wouldn't that have just overflowed from the carbs? (No fuel leaking from the carbs.) Next thought was, did I damage something (air valves?) when I was blowing compressed air through everything? How could it free flow like that?

First problem seemed to be lack of fuel... now... <sigh>

 

Most floats are adjusted by bending a tab so the needle shuts off the fuel when they get to a certain level. Floats can also go bad and leak internally causing them to not float and the fuel never gets shut off.

 

Shouldn't really be able to come through the pump, that has a vacuum operated spring on the inside, evidently more petrol getting through than needed, float needles not seating? petrol pump good?

 

As I wrote the above, it occurred to me why carb/intake for cyl #2 wasn't filled... intake valves were open. :/ I pulled the plug, and cranked it over a few time (ignition switch off). Hardly anything came out. If carb #2 was leaking like the rest, and gas leaks quickly past rings, I'm guessing it's in the crank case now. :/ Now I wonder if I need to change the oil. Perhaps it's time to call a professional.

 

Check the oil level there shouldn't be much of a level change