Thanks for all your input on squishiness folowing my earlier post. I've edited it to add my conclusions, but thought that, as this community is so busy, many people might miss the update. So I thought I'd put it in a separate post as well.
Putting together the comments on my original post with what I've managed to glean from other posts, I've come up with the following "Squishiness comparison" list:
From Squishiest to Stiffest:
The positions of the LadyCup and Lunette at opposite ends of the spectrum seem pretty much agreed upon. The ordering of the others in between is less clear - as lintilla said, it depends on whether you're talking about the bell or the rim. I couldn't figure out where the Keeper fits in this list (except that it's stiffer than the LadyCup), and found no comparisons at all for the Femmecup.
Thanks for all the comments - this has really helped me decide which cup to try next (after my LadyCup saga). I had been thinking of the Lunette. Following this discussion, however, I can see that it's nowhere near the LadyCup in terms of squishiness (I need a soft cup so it won't put too much pressure on my sensitive bladder), so I will avoid the Lunette. The Divacup sounds like it will be too long for me. So I guess the next ones to try are the Miacup and the Mooncup UK.