I was thinking you might want to transplant those in to something deeper. Ice cube trays arent that deep and you want to give them enough room to develop some good roots.
Whelp...that didn't work out well. I transplanted them into their own pots, only to see that they died. I have no idea why. Every single one I transplanted into a pot died, yet the ones that I planted into an egg tray survived. The ones that I've left inside of the ice cube tray made it too.
I'm going to wait until they're bigger to transplant again.
How were the roots in the pot and the dampness of the soil in the pot? Did they dry out? If you have the pots, just start the seeds in the pots so you'll have more room to work and less worry about losing the little root hairs on the roots. I move from 8 ounce cups to 16 ounce cups, and then to the garden. When moving sprouts without true leaves, I bury them in to their cup so just the cotyledons show up about 1/8 inch above the soil and keep it "too wet" to make sure they can get their roots re established.
I hate to take theminside after I've taken them outside. If you have a semi-shady place, and you can block the wind, you could wean them from their "nursery" inside home, then put them in the ground from there, of course AFTER the last frost.