Who says they don't like being "repotted"?
I bought this baby in January in this condition:
6 months later it looks a little more like this:
It's got half a dozen new roots and looks as happy as I can imagine. The only "issue" from mounting it was the 2 spikes that were already there died off. But after 3 months of nothing they were never going to open anyway. It's got another bump that I am pretty darn sure is another flower. I think it likes being on a mount.
As for care, I water daily (it's outside for the summer), fertilize when I remember (once a month or so), and hang it where it gets about 3 hours of (sort of) full morning sun and about 30 mins of the sunset.