As far as adjusting fuel mixture screw, you should set it to the highest possible idle RPM, then richen it up so you have max idle RPM minus 50 rpm. So that is just a sliver on the rich side of perfect. Splitting the difference is definitely going to be rich. The other point you just made was it runs better cold than hot. This is also an indicator that it is running rich. An engine richens up as it warms up. Have you checked the float level and made sure it wasn't set too high?
If the valves were not too tight, they won't affect idle RPM either. The other point you made was running this with the A/F out does not make a difference. It should be way too lean with no A/F. Can you actually rev and ride the ATV with no A/F? It seriously should not be rideable without an A/F.
Now I am curious how long this problem has existed, and what other history you have with this unit? I feel like I need to know more details now. Did this happen all of a sudden, or gradually got worse, or was it ok the last time you rode it, and then it never ran right the next time you took out, and ever since? What?
I am sure there are specs for the ignition but an ignition isnt going to give you a high idle, unless it is mysteriously advancing the ignition by itself, which all you need to check that is a timing light. Compare timing at cold start up to timing when warmed up.