OK. I really need to get some sleep, but this was bugging me. The one setting that I did not re-enter after the downgrade was the port forwarding settings. I did not think I would need to, because I had unchecked the check box a couple of weeks ago. So, I assumed the router was no longer forwarding those ports (since it shouldn't be). Maybe it is, though. I re-entered the port forwarding info, but left the check box unchecked. Several reboots of the Xbox later and the NAT has been open with each one. Now, maybe that check box doesn't do what I think it does (enable and disable the port forwarding rule). I don't know. For what it's worth, here are the ports that I forwarded (they're listed on xbox support):
TCP: 3074,53,80
UDP: 88,3074,53,500,3544,4500
Xbox Live video still appears to be streaming just fine after this change.