Problem solved with a long story.
I had forgotten how I first setup the two 722s and the 625 (it's been more than fifteen years now!). When I set them up, they were all sitting next to each other hooked to the same TV so that I could swap back-and-forth and set them up with the same timers and favorites. To do this I had the 625 set to remote ID 1 and 722s set to remote IDs 2 and 3. After they were all setup, they were distributed about the house And the MX-500 remotes were programmed with the respective 5.3 remotes with those same remote IDs.
Now when I tried to use the old 5.3 remotes with the Hopper, I ended up inadvertently picking the remotes that were still programmed for remote IDs 2 and 3; the Hopper requires remote ID 1. That's why they did work when I first tried them.
After playing with the remotes for a while, with the instructions here, I managed to get a 5.3 remote reprogrammed to remote ID 1, but also accidentally reprogrammed the 722, sitting right next to Hopper, to also respond to remote ID 1 (Again, they are right next to each other to easily copy timers and favorites to the Hopper). But now both receivers were responding to the same remote. When trying to do something on one receiver, bad stuff would happen on the other one; very confusing (and it didn't help that my late night comprehension kept reading the instructions wrong).
After temporarily disabling IR reception on the Hopper, I managed to get the 722 reprogrammed to remote ID 2. then after reprogramming MX-500 remote with the respective 1 and 2 remote sets, I then had full independent IR control of both the 722 and the Hopper.
Whew, what a fiddly mess!
I ended up ordering a spare 20.0 remote because the 5.3 remote doesn't have all of the buttons/functions on it for full Hopper control; mostly the color buttons, options, and some others. The 20.0 remote (which has those missing buttons/functions) will allow me to update the Hopper remote set on the MX-500 for full Hopper utilization.
Thanks you for all the patient answers and reminding me of what I had forgotten. The whole home AV system upgrade continues to the next steps.