I think using your Bitcoin to open Lightning channels, and then swapping your Lightning balance to onchain (e.g. via Boltz) is easier to do - and at least as private - as what you suggest
Doing that is a type of coinswap. And it is awesome, and it is great to see the number of providers grow. I think miners are a particularly apt group to be providers of such a service because they have always-on server, are used to bitcoin as income, and have a steady supply of new sats to treat as merchandise.
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