I use cups, too, but I've graduated with a few "improvements" over time.
-- I have about 10 of the ubiquitous Mirro brand cake pans that come in handy for lots of things. (Get them cheap at your thrift store.) They have relatively high, straight, vertilcal sides that keep cups in place, should they get bumped.
-- also, I prefer to use smaller size cups when I can. Juice glasses work great and provide a lot more stability, and for space saving when I can, I have a stash of those heavier clear plastic party cups a little bigger than a shot glass. I use these for soaking seeds, too, but you want something bigger for lily seed.
Writing on the cups is redundant. Along with the seed pod goes the identifying tag that was on the pod stem.