Nope, upkeep is a static amount determined by research. You can set it to whatever you want with research, but you can't do any checks on the game state to determine it. Sins would needed scripting support for that, which it does not have.

You can eliminate it completely, but you can't have it change dynamically throughout the game. It can only change in response to new research. What has been suggest it is to have individual ships have abilities which deplete resources slowly, so each individual ship has an upkeep sort of like Total War, but that won't be a percentage and the AI probably won't have any clue of how to deal with that.

I personally like it because I think its a lot harsher penalties than most games have, which means when and by how much to increase your fleet size in the most important strategic decision you make. Its supposed to represent things like logistics and military infrastructure/administration, not the cost of actually supplying the ships, so it remains even after the ships are destroyed.

Abilities like Drain Planet and the old worthy cause can be used to gain resources/credits via abilities. I would first try using very small negative numbers on passive abilities.

One thing to note is that it will be much harder to see just how many resources are actually being used up by these abilities. You may have to use the after game statistics to get good data for balancing.