I really feel like I've been sold a bill of goods with Cloner.
I took the advice WPMU gave, to use it to set up MU networks for staging. I just redid a site using that method: clone to a subsite (seemed to go OK), then clone the subsite to the main site.
It's been hanging with no visible activity for 10 minutes.
Thankfully, I made Snapshots of each site before this started. I need to be done for the day in an hour, and this was supposed to take all of five minutes to transfer, then 20 minutes to check over.
Edit: I was wrong. The entire network, including the WP backend, is on a white screen.