It's a few days later because work interrupted me. Got all the data copied in ~12 hours, though one of my old drives indeed failed during the process. Swapped the new drives into the old NAS, imported the pool, relinked my mount points, and everything seems good to go, beyond a brief moment of panic when the NAS failed to boot because I had accidentally bumped the SATA cable to the system pool SSD.
All in all, not too bad. Now I can use the remaining functional old drives for some kind of longer-term backups. Appreciate the advice, guys.