Me, too. In my first year WSing I tried some shallow deli containers, peat pots, and paper pots, and none of them worked well. They just dry out too fast.
Pippi, the biggest difference in outside and inside conditions, is that outside the sun and wind dry the soil much faster than happens in controlled temps, air flow, and no sun in the house. Those cell packs only hold a few tablespoons of soil and that small volume can dry quickly.
Shallow containers work fine in the house. Most of the time my trays inside are only about an inch deep.
Karen