GC - great photos of the Kunzite. From what I can see, that's a great cut and highly unusual. It's obviously been cut by a master cutter and on that basis, I'd hang onto it. What I might be tempted to do is see if there is somewhere that would be able to heat the gem to see if it can be pinker (if it bothers you). Holts who are based in London have their own gem school and I think might know where you could send it. I've seen some of their work and I'm not 100% sure I'd want them to do it - others may have a different experience but some of their cutting is, ummmmm, errrrrrr, well, you get the picture! I'll also ask Luke because he may know of somewhere and will PM you if I get any news.
As for the Alex - it's a native cut alright but, without having it re-cut, you could actually have it re-set and then it would sit tighter in the setting. It looks very much like the claw on the skinny side of the gem is too high and doesn't fold over as much as it should - couple that with the notch the gem is sitting in is probably too wide and you'll definitely have a wobbly stone! It's easily rectified though and shouldn't cost much. The only other thing I would add is that a huge proportion of Alex is cut to maximise carat weight and not beauty unfortunately so having a native cut shouldn't be too much of a concern.
Has that helped?