Normally a bit of movement does not hurt it.
An FX 6300 should not run that hot on this cooler unless very overclocked.
You could try to reinstall it. It may be worth applying a very thin layer to the cooler base just to ensure you fill any gaps. The new 212's should not have any gaps, so if yours is like that just skip that step and give it another go. I know it is a pain, but that cooler can do better for sure. Remove the fan while installing to make it more easy to handle the cooler. Just support the tower when you install the fan after.
Also make sure your fan is running at a proper speed(your board should manage this to be honest.).