Might as well put the egg cartons to use! If they're the paper kind, they aren't much different from the little cups they sell for seed starting; the ones you can put right into the ground when the plant is nicely rooted. I'd think you could just cut the bottom out of the egg carton section if you want to be sure the roots can get into the soil and not have to wait for the carton to break down sufficiently.
The ones I have are not only paper, but most are from an organic kinda company - they were on sale. I'm thinking they'll hold together long enough for me to get the seeds in the ground, but not much longer. So...that's good, I guess.