The way things are now, Governors are in no danger of being overpowered. More like never used. I think that Path of the Govenor should give you a +1 exp per city level per turn bonus (managing a bigger city is more difficult, therefore more exp), but preclude you from having access to some of the more powerful combat skills that are available after you choose your path. When considered over a period of time, 2 or 3 exp per turn isn't really that much experience, considering that a combat champion can gain hundreds of exp in one fight. Govenors don't need a boost, they need a crash cart. I think they are a neat idea, but they are too useless to even be properly tested and balanced at this point. They do need more skills though. I think no one has realy given much attention to Governor skills because so few people even bother using them.
An alternative would be to change the Adventurer's Guild so they give +1 exp per turn, are buildable in multiple cities, and perhaps even be upgradeable to +2 or +3. I'd have to have a closer look at the numbers to see if this would actually be OP or not. I think it just sounds OP because the current incarnation is so underpowered (aka useless). I have never ever EVER built one and you would have to be really bored or on glue to think it would be a good deal. Think about it. They are only useful if you leave a champion there doing nothing or governing. Why would you build them in every city if your champions are always exploring? You build them where you plan on stationing your Governors for some time. There are far easier ways of gaining exp for combat champions.
One or the other of these, maybe both, would make Governors a viable strategic choice. Other suggestions, like a penalty to combat exp are good, and work within the existing system. Basing exp gain off of total city output might be difficult to balance. If you really tweaked out a city, it could yield crazy exp, not to mention making the calculation understandable to players. City level scales well, has a predictable maximum and pacing and encourages governing the major cities, not using governors to supercharge your spammed cities. You could still move an experienced governor to a small city, but you would sacrifice potential experience to boost a smaller but strategically important city. That sounds like a tough decision, which is what makes good strategy games.