OK -- an update. Since it looks like I'm going to need to swap my 722k, I thought I'd back up the timers. Oddly, the system said that the remote appeared to be from a different system, and offered to restore things, which I didn't want, since the backup was from December. Might even have been December a year ago. I then registered the remote with the receiver, and it exited. Went back in and this time had the option to do a full backup, and it claims to include timers (though who knows if the restore will include timers!).
These menus are different than when I tried to restore things in the past, so I can see what the response above was about. I'm hopeful I won't lose my timers when I swap the 722k, but not optimistic.