You can improve Bitcoin privacy by running two Lightning nodes over Tor. Fund a channel between them with KYC bitcoin, make a partial payment across the channel, then wait a few weeks before closing it. The payout goes to fresh addresses with no direct on-chain link to your original KYC coins.

Elaborate?

a -open-> LN channel(b,c) -close-> d,e

Heuristic: d and/or e through b,c belong to a?