Looks like sun scald to me. I cover my tomatoes with a white cloth when it gets too hot.

Black bottoms on tomatoes is generally Blossem End Rot, a condition usually associated with uneven moisture and/or calcium uptake and distribution. Sometimes excessive heat. Did you use Dolomite lime when you set up your Earth Box? What type and how much fertilizer?

suncitylinda,in the pic the fruit is rotted on the side not the bottom leading me to believe sunscald

you only got 2 fruit ? sounds like it was too hot to bloom and set flowers/fruit

"Either they have these ulcer-looking sores, or they only developed half a tomato, with ulcer-looking black bottoms."

Dickie, I believe Suncitylinda was indeed addressing one of the OP's concerns.