Have you used #Loop?
Whenever discussions about bitcoin and kyc come up, I'll often see comments about Coinjoins with Whirlpool, or more about just not using kyc. These are great of course, but I rarely see comments on my favorite way to deal with kyc bitcoin, that being Loop.
Step 1: Have a lightning node. Great idea generally.
Step 2: Get on-chain bitcoin. Preferably above 0.01 BTC. Let's assume it's tainted with kyc.
Step 3: Make a lightning channel with a well connected node. ACINQ, Wallet of Satoshi, breezy, someone with very high connectivity.
Step 4: Loop out all of the funds from that channel to cold storage, except the channel reserve and active funds you're gonna use for zapping people/buying goods.
Congratulations you just broke all on-chain trace of where the hell your money has gone. And that's not all. You can come along and loop-in -> loop-out more kyc funds later, and those are even better off because they aren't indicated to be part of a channel with any connection to you.
As for fees, I haven't done a direct side-by-side comparison against whirlpool in a while, but it averages 0.35% for each side, or about 0.7% to loop in and then loop funds out.
Hope you find it useful.