For anonymizing larger amounts, where Lightning might not be the best fit, I think swapping into XMR and then swapping back into BTC on-chain in multiple time-delayed TXs to different addresses might be another way.

Should we split XMR>BTC swaps into common UTXO sizes like those used by Whirlpool? That would help make it harder for the swap provider to pick out an individual and their resulting UTXOs.