Iced up coil usually means you left the freezer door ajar.
You probably jammed too much stuff in and it didn't shut properly.

It actually wasn't that full and the door was shut all the way. As a
point of reference, it was the evap coils (not the condenser coils)
that were iced.

The timer is on the bottom. Look again.

On the bottom where? On the bottom inside the freezer? On the bottom
outside behind the unit? On the bottom in front of the unit?