I've moved huge chunks of hosta and have also split clumps down to small pieces during drought and high temps without losing them...the bigger clumps barely even noticed once they were watered in. The smaller ones should probably get back into the ground the soonest, however, because their thinner bases won't hold water as long.
Daylilies should be fairly easy to move safely. I've dug them for transplanting and left them lay (unintentionally, of course
), covered in moist compost for up to two weeks before replanting and they were fine.
Transplanted peonies here usually take about three years to re-establish and produce blooms.
I think I'd pack lily bulbs in dry but not dusty peat, inside paper lunch sacks marked with the variety name and leave the tops open a bit - then, if you have a bunch of them perhaps place the marked individual bags inside a cardboard box with holes. If you need to trim off this year's growth yet, I'd let those bulbs dry a day or so before placing them in the peat.
Good luck!
