SUCCESS!!!!!
Before I get to what I did to have success, I'll answer my two questions above for future reference.
First off: Once successful, timers show up immediatly
Second: Message 1001 and full system restart did NOT happen for me when successful. I got short message saying Restore in Progress with a black screen, and then live TV.
Ok, here is the solution I had. It took a 2hr phone call with Dish Advanced Tech Support.
So, first off, we did a "Partial Reset" on the H3. Neither myself nor the Tech thought this step was necessary, however, we did it anyways.
After the partial reset was complete on the H3, we went back to my HWS. This seemed to be the problem. My HWS was on the OLD UI. Aparently even when doing timer transfers via remote, both hoppers need to have the same UI. Soooooo......we had to update my old hopper to the new UI. To do that:
Menu>Settings>Diagnostic>Updates. Once there, Press the Play Button TWICE, and then Recall (All still using the 40 remote). Then the new menu should have the option to "Download Now". Select this. It will take about 25 mins to do it all. Once done, the HWS menu will look just like the menu interface on the H3.
From there, we did a fresh backup to the remote on the OLD HOPPER (HWS). (Menu>Menu>Tools>Backup Settings). Once complete, unplugged turned the H3 back on.
Once the remote was re-paired with the H3, Tools>Restore Settings>Restore to Reciever.
Note, that it still took 2 tries as outlined above to get this to work. First try failed. I had to go back to the HWS, rebackup and try again.
SO......it was either the UI difference OR the Partial Reset that fixed my issues. But bottom line, I am all good now!!!!