Fourtrax 300 Issues

Hey geys new to the forums!

I have a 16' rancher 420, and i believe a 91 Fourtrax 300.

I got the 300 from an older lady who had it and it sat for a while. When I brought it home it would start up perfectly using almost no choke or choke for a few seconds and would idle all day fine. However, when i got on the throttle the carb acted like a 2 stroke in which it had very low power on the low and middle rpm band but would pull fairly strong in the upper rpm's. I immediately replaced the spark plug, oil, oil filter, and discovered there was no air filter so i put one on it. This made a good difference but it still wasn't perfect so I automatically assumed the plastic piston in the carb was probably scratched up and sticking so i ordered a whole new carb instead of dealing with rebuilding it (43$).

Now with the new carburetor the situation has reversed. It has great pulling power in all RPM's (My 420 barely pulls away from it now) but will not idle correctly and its backfiring upon deceleration. It also seems upon steady state cruising to cut out and bog for a few seconds until i heard an audible backfire then it resumes normal operation.

My question is am i looking at a jet problem or possible choke problem? i reused the old choke cable but the choke jet (i guess thats what it is) was different than the old carb and not the same length so there may be extra tension on it even with the switched fully open.

Thanks guys I love Honda (got 2 honda cars as well) and im planning on getting a 350 next weekend!