Thanks for the advice! I tried a few different solutions for the velocity and ended up with an equation that takes a normalized charge, then raises it to a power, then multiplies it by the direction vector and a power multiplier (Probably pretty close to what you imagined). So you could say it's intentionally unintuitive in some ways. But I used this scrappily to effectively expand the power ranges where you can hit a lower-power shot and still be able to hit a more powerful, exponential shot.
I had no idea KE was calculated like that, honestly really useful to know. That would explain why each similar variation still felt wonky. If I could will myself to touch this game again, I'd go back and try to implement a solution like the one you gave. My excuse is that I haven't taken physics yet, so....
I hope you at least enjoyed it a bit!