So far I've only put him on whisper, generally speaking I name a ship with higher ps than whisper or a ship that can attack more than once.
Whisper may benefit from naming the ship with a TLT as his Kallus target for the very reason you listed. 4 unmodified green dice suck. It sucks even more when you have to spend a focus on defense for only a single eyeball only to roll blanks and eyeballs on your next roll.