I'm not a free play person, IMO get rid of it.
Make sure your front sprocket is tight, make sure you have about 3/4 to Inch of chain slack.
The chain pushed on the bottom side, middle between sprockets should have 10-15 mm of space before it touch's the swing arm.
You can put a throttle tube on, reduces amount of cable movement first 1/3 of travel.
Never looked at the TPS before, don't very few issues. But how about the bodies being balanced. Your only 10 out from each other. 10 is very normal getting it perfect is next to impossible. Once done, don't expect it to save.
I think real issue is in the balance we need say 41.2 41.9 52.1 No decimal points to see how close to next whole number so they bounce.
IMO. Pull the tank, check your plugs. How do they look. Pictures please.
Check all the hoses.
If you find a OH BOY then fix and test. Nothing pull bodies, start over.
Tank loose, I used a hard foam block to hold tank up off bike for room to adjust and spray around for leaks.
FYI.. DANGER Carb cleaner if flammable, reason things smooth out it blocks leak and it burns. Having pools or any visible amount laying on a hot running motorcycle flashing it off into a gas will easily ignite.
Have a fire extinguisher around, never ever a bad idea dealing with a gas tank. Have had a connect pop off and leaked a bit before sealing, and do it out doors. Bike goes up garage, house doesn't.