The masses of the involved objects are way too low. We thus know for sure that any gravity effect is negligibly small.

I think you got what I meant by that last quote, because you explained it very well.

The negligibly small gravitational effect is what I had in mind as a possibility for it to be detectable in the future by some precision enhancements. (I have no idea if that can be possible, was just a thought)

From what I understand on how the momentum detection happens, is by measuring the radius of the curvature and the arc length of the charged particles' trajectories?

So in principle, if we can get super precise, even the tiniest gravitational effect should have an effect on the angle.

Hopefully I'm not way off with my understanding about it :p