I don't know why the engine would turn freely with the plug removed and not with it installed but I have to disagree with it being a valve timing problem. When the valves are timed correctly a 4-cycle engine has maximum compression on 1 upward stroke of the piston and a 2-cycle has it on 2 upward strokes. Any valve timing problems would result in reduced compression, not more, as one or the other of the valves would be open or partially open during the compression stroke. Maybe there is a problem in the recoil starter which is magnified when the engine has good compression. Just my 2 cents.
Bob B.