A worn or binding kicker can make it kick strange through the travel and be inconsistent. I am not under standing the "pushing" hard its in neutral or not. I agree that a worn clutch basket (or warped) plates could cause it to drag but in my experience that is quite consistent.
Smartie, any photos might help us figure it out.
A couple things to try, check the chain, it could be too tight, rear wheel bearings, and pull the chain off and check the output shaft, a bearings with a broken cage could have the balls binding up.
Also loosen the clutch cover, and see if that makes a difference in any binding.
Cabmkr