What happens if you run Patterson Beams?

I'm not sure why the F (last note of 2nd triplet) has a longer stem than the G. (last note of 1st triplet)

I've only used Patterson for beaming over barline. What would it do?

It'll lower the beam of the 2nd triplet getting rid of the white wedge. Try it, if you don't like it, then undo.

I don't mind when beams slope (under Document Options I have the max beam slope set to 6 EVPUs anyway). I was hoping for the tuplet number 3 to float at a universal height, regardless of slope. They vary quite a bit and I have to spend a lot of time tweaking them.

Instead of manual placement, try changing it to stem/beam side.