Unfortunately this is no good news for solving the lower bits puzzle transactions if I understand correctly:
If ALL unconfirmed transactions in mempool are RBF enabled there will an overbidding fight for lower bit-puzzles even if initial transaction has set "NO RBF".

I didn't understand what you mean exactly but when you send a transaction just set it to no RBF, and that's it. If someone attempts to send the coins again, it'll be flagged as a double spend and nodes won't broadcast it to miners