Let me get this straight...

If you play bullet chess and hang too many pieces the server interprets this as an attempt by you to deliberately lower your rating and you get banned?! Well there goes my chance to try bullet chess for real. I guess I'll have to stick to rapid (10/0 or more) to avoid getting banned for making honest mistakes for wanting to play bullet. Is this Lichess's policy for real?

I don't think the server counts hung pieces. AFAIK, it counts losses in very short games. Try to keep a fight for at least seven or eight moves.

You'll be fine, don't worry. The lichess system rarely makes mistakes on the part of sandbagging/cheating.

If you're hanging all your pieces, maybe bullet isn't enjoyable anyway.