I finally got my replacement LilacCup in the mail today (Lunette Selene still nowhere in sight). I thought I'd comment on the difference between the cup that split and the cup that (hopefully) will not.
My new cup is a much richer color than the one that split. The new one is like the original LilacCup in this post, whereas the one that split is exactly the color of the trial cup in that post. Also as that post pointed out, the trial cup is way stiffer than the new one. The same is true of my split cup.
I'm not due to start bleeding for around two weeks and dry runs are more trouble than they're worth for me, so I won't be able to test everything out for real, but today I was going to watch my DVDs of The Office and practice all the folds again (nice way to spend spring break, says I).
I'll edit this post this evening with my verdict, but it appears that the splitting issues have been resolved.
UPDATE: After folding it off and on for the whole day (and doing it none too gently) I don't think this cup will split. It has withstood firm folding and violent popping open, all current folds, and some ridiculous experimental folds. Thumbs up. /UPDATE