If I have interpreted your post correctly, your engine must have a different carb to any that I have seen on a GMS. On all the ones I have seen the throttle arm ring (which is attached to the throttle rotor with a set screw) is the same diameter as the rotor and does not bear against anything on the carb body so cannot control end float in the rotor. In any event it moves away from the carb body as the throttle is opened. Even removing the throttle arm ring completely wont change the end float.
The end float of the rotor is determined ONLY by the clearance between the stepped end of the screw in the top of the carb and the scrolled slot machined in the rotor.
A bit of clearance here should not present a problem as there is, of course, a spring behind the rotor which will load the screw against one side (the inside) of the slot at all times.
The critical setting is the position of the idle needle relative to the end of the spray bar tube at full throttle with the spring loading the rotor 'out' of the carb body.
I agree with you comments re the design and getting what you pay for!!