I went to Ross and bought a package of 6 cooking sheets which
have about a 1/2-3/4 inch lip all the way around. They are really
cheap and work great for putting the cups in. You can bottom water
in them too if you want. I stopped using the black plastic flats except
for germinating under domes 'cuz I don't water much when they are
germinating:
Also, instead of making a bundh of holes in the cups, you can use a
box knife and cut four drain holes on the side of bottom of the cups
in about 3 seconds. Seriously.