THHW will be illegal unless it was also rated THWN or something else approved for wet locations, but most of the stuff out there these days is.

Your voltage drop estimations sound reasonable. Even at 60 it would be OK, you'll have less drop owing to the fact that your actual current flowing appears to be less than 30 most of the time (assuming your 120V loads are distributed across both legs).

The new building will need it's own grounding system (rods).

Sorry, the conductors are THWN wet rated, I typed it wrong.

Just a follow-up.

I checked amp's at the Sub-panel and with everything running and had right at 20amps per 120VAC leg. Checked voltage at AC recep. with AC off: 120VAC; with AC on and compressor running 118VAC.