Very frustrating motor issue - 2003 Yamaha T60TLRB

I have spent alot of money and time trying to get this motor back to running normal. Here is the situation, any help is greatly appreciated. This is a 4 stroke 60HP Yamaha High Thrust.

Issue:
idle to about 3500RPM motor is hesitating and popping in the intake. At idle motor will shake your teeth out. Weird thing is at high RPM motor runs fine. I think initial cause of this was at one point i left gas in motor sit to long.

What I have done:
- had a local shop rebuild all 4 carbs. Spent $900 but motor ran just like it did before i took it in. Not sure if they actually did anything.
- pulled head, had it reworked and checked. Head was resurfaced, new gasket, set valve lash to spec, etc.
- Rebuilt all 4 carbs multiple times
- New fuel line
- new spark plugs
- tried re-syncing carbs but bottom carb wont sync
- leak down test is fine on all cylinders
- pull plug wire on bottom carb and no affect to motor
- pretty much seems bottum carb is not firing at low rpm
- new coil packs

My guess is the bottom carb needs replacing but it has been rebuilt multiple times.

Here is a video of the motor running and vacuum gauge on each cylinder/carb:
Motor Run Video

I do not know if this could help, but I had an older inboard with the same similar issues. $4,500 later from chasing the problem it turned out to be the harmonic balancer .

The list of things that have been done, are they things you did or had done?

If the carbs or a carb wont sync its probably a problem, to me the answer "it wont sync" is not acceptable from a professional. Take it to someone who knows what they are doing and get it fixed.

Have you checked the spark? New plugs don't mean your getting fire.

One carb not syncing could be an issue with a valve not opening when it should on that cylinder. Of course it could be other things too but the popping in the intake seem to me that something is out of time on one cylinder. Might be worth a look at the valve train on that cylinder, rocker arms and adjustment nuts secure, cam followers and cam lobes on valves. Valve spring broken? bent push rod? Any ticking noise at idle?

Oh, and a valve lash adjustment too tight could screw with the vacuum read too.

Check the bottom crankshaft seal.

Thanks for everyone's input on this. I was able to work on the boat a little today. I double checked the valve lash again and everything was spot on. I did loosen up the #4 cylinder lash a bit and did get a better sync on the carbs. Things are running a little smoother, less popping in the intake and a smoother idle but still not 100%. I am wondering if the resurfacing on the head needs looser lash on the valves. I don't think it was much of a cut down on the resurface from the head shop even though it was pitted pretty good from corrosion. Who is the best Yamaha shop in Houston, may just need to bite the bullet and take it somewhere. It is hard to start when cold, i have to throttle up a bit to get it started. Once its warms it restarts fine. Number 4 plug is sparking fine. Motor does run good at high rpm.

If the valve lash was too tight you might have a slightly burned exhaust valve. Maybe a little hard run time will help lap the valve in better??

where you located

Cypress (NW Houston)

That #4 carb has 2 mixture adjustments 36 & 37 one has to be idle and the other main mixture. http://www.boats.net/parts/search/Yamaha/Outboard/2003/T60TLRB/CARBURETOR/parts.html

Carbs on the four stroke outboards need to be synched using a VacuuMate instrument.