Piggybacking off this, I’ve found it fairly cost-effective to go from Lightning to Muun for an on-chain swap, then Muun to hardware, where you can set the miner fee.
Agree you have less (no) control over utxo selection with Muun, but since it’s a submarine swap anyway (which I only partially understand) it gives me a sense that privacy is enhanced already. Well worth the slightly higher LN fees to send into Muun!