It seems from the few times I have tried tomato seeds in shallow containers like egg cartons, they have had a better germination rate. That is why I intentionally sowed my first crop of tomato seeds yesterday in larger deeper containers, but less than half filled with soil. The idea is to get them to germinate fast , then slowly add soil around them as they grow. This should help avoid the fast drying out. I still plan on having to transplant them at least twice before going into the garden, tomatoes seem to benefit from that. I have high hopes for this, but it may be a total flop.I have my tomato containers on top of the freezer covered with a piece of glass.Just started them yesterday.
The only reason I can attribute to the better germination in shallow soil is heat, I think with a low heat like on the top of my freezer it heats up a shallow depth of soil better, where as a deep soil level never gets warm enough, just my guess.