Back to a major carb clean and set. Trying to fix external bits in an ad hoc manner will leave you chasing your tail and drive you crazy - and not fix it.

Go back to the basics - make SURE the carb is RIGHT.
Make SURE the spark is good and strong with a fresh spark plug.
Make SURE there is good compression.
Check the timing!
Then see what happens.

Is it also worth checking the air filter?

Supermotodave, your profile doesn't say where you're from, but here are a couple of sites that may be useful in identifying your TT600 and for buying new parts:

https://www.fowlersparts.co.uk/brows...aha/bike/tt600

https://en.impex-jp.com/catalogs/moto/yamaha/tt600.html

check the air filter, but unlikely to be the cause


that bike shouldnt have a vaccuum pick up point, but who knows, might be drawing air from somwhere, check that there are no suspect un plugged tubes on carb or manifold


did you try to raise the idle screw?

Is the fuel enrich circuit actually flowing fuel when the knob is pulled? Bike will normally run for a few revolutions when cold and no choke. I would unscrew the starter/ choke knob from the carb and ensure all is working correctly.

Is pilot jet really clean? Even when you think they look clean and you can see through it there can be a layer of old fuel varnish that is very hard to remove out of such a small hole. Many an idle issue on my bikes have been solved by tossing the "cleaned" jet with a new pilot jet !

Greetings:
I have a 94 XT 600. Mine sat for about 15 years. Suffered the exact same symptoms. I took the exact same repair steps. And I got the exact same results. The carb is indeed a bitch to remove/replace. So after the first time out I opted to clean the carb in place. Easy & effective.
Buy a can of aerosol carb cleaner.
Disconnect the fuel line from the petcock. Leave the hose connected to the carb. Spray the cleaner into the hose until the hose is full. Crank the engine a bit to suck the cleaner through the carb. This takes a bit of time and cranking. Keep the fuel hose full of cleaner. Let it sit for some time. Over night for example. The purpose is to keep the inside of the carb soaking in the cleaner. I had to do this a few times. And I had to keep adding cleaner to keep the fuel hose full. I guess it evaporates out the hose. I think I actually found a small funnel that fit into the hose. The kind if funnel used for filling old kerosene lanterns. I filled the funnel and laid a bottle cap over it to slow the evaporation process while the carb was soaking. Slowly but surely things improved. I also kept a battery tender connected since this is obviously hard on the battery. A hot battery is a must when these brutes are cold. Also, safety glasses are a must when spraying the cleaner into the hose. Chances are you will get a face full of cleaner at least once. I am a bit slow. I got it two times. Then I found some safety glasses.
This took a bit of patience but it beat the hell out of pulling and replacing the carb multiple times.
After I finally got her running and put some miles on her she now runs great. Still takes a while to start after sitting for more than a few days, but it does always start. Also, my choke is very finicky when cold starting but it always fires immediately once it is warm.
Best of luck to you.
Marty