I spent all last summer fighting a 85 125M, you can see it in my avatar pic next to my 200ES.
I had problems exactly like you, would only run with choke, was really finicky to get it set, etc. Check the plug, see if its running lean, i suspect it is since your using the choke and needle settings aren't helping. You most likely have an intake air leak.
I finally bought a new aftermarket carb off eBay and toss that on, was a huge improvement but still had a minor stumble and tuning problem, turned out to be the gasket between the intake tube and the head and the gasket between that carb spacer/heat insulator and the intake on the other end. They are just cardboard type gaskets. I bought some gasket material from Napa and used the intake tube to trace it out for the head end and what i scraped off of the old gasket to trace the inside opening, etc.. The other end is easier as you can use that spacer between the carb and intake tube to trace a gasket. Also make sure the o-ring on the front of the carb is good.
After i replaced the gaskets it literally fires on the first pull, choke is only needed if its really cold, on a warm day it pops right off and is ready to run.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....