Trust me, if your influence is in the positive, always sell influence for money.
And I think you misread the card or something, there are 3 donation cards that gives you money for influence (small = 10, common = 20, generous = 40) like their exchange rate is 1:1(unless in hard/impossible), I don't know any card that has worse exchange rate than the influence overflow.
I always use these red donation cards when I draw them. Due to this, I was very rich (300+ money) in normal, hard, and mid-game impossible mode. And with good water carrier placing, my influence never made it to negative in normal and hard mode.
I see. In that case, I suppose my real issue is I thought 100% approval was the goal. Like. It's water. If people in a certain block are only getting 50% of the water they need to survive, that's a problem that will literally kill townsfolk if it lasts for more than a day or so. Anything less than 100% is a failure state.
Or at least, that's the way water works in real life. It never occurred to me to treat overflow like a problem to be solved or a resource to be spent. I thought overflow meant nobody died this turn because we met quota and maybe went a little over. Sure, we could try bartering away some of the excess, but what if it makes us come up short? Too risky.
I feel like I'm starting to overstate the point, but if only 90% of the people have water, 10% of the people die of thirst. That's how water works. It's one of three core mechanics of IRL literally all of us learn during the tutorial level. The game's influence mechanic feels like a weird abstraction that doesn't make sense in the real world.
Influence and money are concepts in the real world, to be sure, but killing 10% of the population per day for money seems like the kind of thing that wouldn't be feasible for very long, even by medieval standards. If the peasants didn't revolt, at some point, you'd run out of peasants.