...could I incent the bees to move up quicker by putting two full frames
Bees occupy the box if they are strong enough to do that. They warm up brood area and they do not leave it. Like Michael says, bees abandon brood in lower parts of hive if they are not able to keep them warm. They eat larvae away and tear open pupae.
If hive is not strong enough, I put extension box under brood area. They they it into use when they have enough bees.
When you have 2 boxes, it is same where bees put honey. - Inside, I hope. 2 boxes is not yet real hive. It should have 2 boxes for brood and the rest honeyboxes.