In a high fees environment:

Buy BTC and exchange it for L-BTC at no cost for example on Bitfinex.

Transfer L-BTC at no cost to your multi-signature Blockstream Green wallet or Jade.

Wait for the rates to go down, and when it happens exchange L-BTC for BTC on sideswap.io for a 0.1% fee and send it to your cold storage, with all this on top you gain privacy as you leave no trace on the chain.