Adding skills to the govs is a good idea, it should make the govs more interesting.
But you know of course that there is a real dichotomy concerning the path of the governor : levelling.
Why not add, first, a city improvement that the player would build in the city where he plans to put a governor ? This building, call it Governor's Office or whatever, would provide xp per turn to the stationed Champion (if you can, you should restrict it to a Path of the Governor champion, of course). It could also provise some other bonuses ...
I think this improvement would achieve your governor's boost.
Or would not