I wonder if the removal of any or some of the vacuum lines might be part of it. I am purely guessing. I have zero experience working on CA bikes.
As we've all stated, it's odd that the symptoms are the same across all four carbs. It would seem like there might be a common denominator causing them to act that way. I know I'm stating the obvious.

 

The vacuum lines just operate valves which 'turn on and off' flow of vapor from the canister to the intake. The vacuum lines are capped.

Yes, it bothers me too that the same symptoms seem to appear across all 4 carbs. I did read recently (and I should have though of this) is carbs 1 & 2, and 3 & 4 have cross passages linking them together. So if one floods, it's possible for it to seep into its neighbor.

I have removed the air horns and will see if all 4 over flow through the top vent or if it's just one or two.

 

In your 1st video, you show the sync gauge and it looks pretty good. The only thing is, the choke is still on. What does the gauge set look like with the choke off? I understand that you have to rev it to keep it running. But even at that, all cylinders should be in unison if the sync is correct.

 

Attached clear line to the float bowl drains, and removed the air horns.
Got some very interesting results... and more clues...

 

I don't remember looking at the gauge after removing the choke. I will pay attention to that next run. I am currently trying to update my theory(ies) based on the results documented by the last 3 videos.

It appears that when it's in 'getting little fuel' mode, it stays that way until I shut it down. It also looked like air was being drawn in via the drain lines. After I shut it down, fuel immediate filled the overflow tubes, and when I restarted, fuel began flowing out the top vents.

Could there be a vacuum or pressure differential keeping the float valve closed or pulsing, and then when the engine shuts down, it releases allowing the float to drop (valve opens), filling the bowl. Then with subsequent starts (and full bowls), fuel flows non-stop?

Now starting to sound like maybe a blocked vent line that equalizes pressure in float bowl.

 

Try removing the cap from your aux tank the next time you start it. I don't think will make a difference but you never know. While you are doing that insure all your aux fuel lines don't go below the fuel pump. I doubt that will affect anything but it will eliminate variables since you are leaning towards vacuum issues. This mighthelp to gravity feed everything.

 

Morning ,missed quite a bit , forgot all about it being a Cali bike , maybe look at all the air hoses

Edit just learnt Evap bypassed

 

Has the EVAP purge control and the EVAP air vent control valves been taken out of the system

 

Yes they have. The vacuum lines that purged the charcoal canister were removed and the vacuum inlets capped.

 

Maybe I was just looking for a fault there, are you going to bench check the carbs for float height, would advise placing them in a container (to catch over flow) attach the Auxiliary Tank to them and see if the fuel gets past the float needle, if thats OK then we know the answer has to lay with a vacuum maybe inside the float bowls while attached to the engine, and just to check there are no Evap pipes running to #1 and #3 inlets and your sync tuner is there instead , sorry to keep asking inane questions