I bought a 2001 1200 sporty and it has mini apes on it. I feel it would be better to have them hard mounted to the trees. I don't think I like the movement although small it is strange. I have a electraglide and I know the bars are mounted the same way and have movement but I don't notice it in the eg.

 

if you can ,have some one turn (lathe) some spacer for you, instead of rubber bushing?

 

+1 on turning

 

You can buy hard urethane bushings for your Sporty that will get rid of the flexing you are feeling, the original bushings are probably shot.
Mine don't flex and I have urethane bushings in mine.