We are tearing down the shift linkage on our '71 with plans to replace all of the bushings and restoring or replacing any worn parts in the linkage from front to back.

It was so nasty dirty when we removed it. We want to clean it up and have it all looking as sharp as possible. Would powder coating it create a problem? We are not interested in originality.

I would. When you buy upgraded linkage from some of the vendors, it comes powder coated.

Power coating will make the rods too thick to slide in the plastic bushings.

The powder coating MAY make it too thick to slide in the bushings, but the bushings can be opened with sand paper. Also, they have been pretty slack with poor tolerances so likely not an issue.

Its a good idea overall that doesnt cause any issues that cant be easily solved.