I've stacked the new bin atop the old, with fresh wetted cardboard bedding and thawed out food in there. Left it alone for two days, not wanting to disturb the worms too much. Checked on it yesterday- already there were worms in the new bedding, and when I looked through areas of the bin away from the food spot, found more worms coming up through the lower bin holes, just like they're supposed to.
Not sure how long it will take them all to migrate, but I'll keep checking every few days. In the meantime, leacheate continues to drip into the tray a bit, I'm just wiping it up and squeezing out into the fishwater bucket for plants.