The only thing I don't like with this option (2) is that most of the coins will move from wallet A to B in in close moments of time.
It's easy enough to space out the process using Sparrow. You can simply enroll one UTXO now and wait for it to land in the new wallet, and then wait as long as you want before starting the process on the next UTXO. You don't have to enroll all your UTXOs in the process at the same time.
You can also freeze individual UTXOs in Sparrow which will pause their enrollment in free remixes for as long as you leave them frozen. Simply unfreeze them again and they will start to be remixed once again.