Got it all back together, filled it with water to cover the laterals, slowly added 325 lbs of "new" sand, and started it up (ran it in filter for a minute, then backwash for 5 minutes, followed by a 2 minute rinse.) The initial startup blew done cloudiness into the pool, but it seems fine now.

The new motor seems to be working much better than the old one too. Debris is no longer floating by the skimmer any more!