Hi everyone! WOW! What a great response to my enquiry!
I greatly appreciate ALL the posts, really. A lot of great information, suggestions and ideas to ponder.
To answer a couple of people who asked this: I am in the US; southern California, to be a bit more specific.
I am 100% certain--at least in my case--the issue was with the most recent update (6.1.0.9)
After making my original post, I had realized that my other PC also has StreamFab installed, but I hadn't updated the program. It was running 6.1.0. Using that PC with that version number, Amazon was working perfectly. Since I have the 'extended download service', I incrementally updated that PC. I did an update, tested Amazon (and a few other services: HBOMax, Netflix, etc.)--all worked fine. Did another update, tested, all worked fine. I did the incremental update process from 6.1.0 to 6.1.0.8--and all is now working fine.
I then went back to the my other PC (the one that was running 6.1.0.9) and took cats4u's suggestion and completely uninstalled/removed StreamFab from that PC. I use a third-party program called Revo Uninstaller 5 to do the actual uninstall (it uses StreamFab's uninstaller, but then does a very thorough and very effective 'cleaning' of any and all 'leftover elements' of a program--folders, files, registry entries, etc.).
I then did a fresh install of 6.1.0.8 and just finished testing Amazon, HBOMax, Netflix--ALL is working fine. I was able to download that Mutiny on the Bounty rented video for my father-in-law with NO problem.
As I said at the start of this post, at least for me, rolling back to 6.1.0.8 solved the issue. So, I think it is safe to conclude the issue is with 6.1.0.9 (at least for me).
Thoughts from the group?