First, my problem got solved thanks to some friendly and helpful people. Thank you, friendly and helpful people.
I think it's too early to take this as a user unfriendly move by Amazon. Historically DRM comes first and then ways around it come next. Hopefully that will keep on happening. Amazon seems to be following a kind of natural upgrade progression. Nothing about it seems to be anti-backup.
I mentioned my calls to Kindle support some time ago and it might be worth mentioning them again. I've been making Mobi copies of all my Kindle books and using Send to Kindle to send those to my devices instead of downloading the originals. I depend on my relationship with Amazon, living in a rural area and not having a car, so I called them to make sure they wouldn't see this as something that would get me in trouble with them.
The support guy I talked with had no idea so he said he'd ask around and call me back the next day. He did and he said no-one he discussed it with could see any issue with it, including supervisors, and that some of the people he asked were also doing something like this.
Then about a year later I read some articles about people losing access to their accounts for various reasons and I got concerned again and made a similar call and got similar results.
This was nothing official from Amazon. They didn't quote policy to me. They just explained that nobody there really cares. They're concerned with dishonest people, not customers protecting themselves. That's my phrase. I don't think they actually told me that but it was the feeling I got while talking with them.
Anyway my guess is that Amazon really has no problem with us doing this.
It's probably also worth relating something that happened to me with Audible in their early days that kind of illustrates the same thing. They limited downloads to 2 devices at the time, which was inconvenient, so I made MP3 versions and used those. These were audiobooks I had bought and I didn't share them. I just made things more convenient and safer for myself.
In their forum in a discussion about problems with the 2 device limit I mentioned that I was doing this. I quickly got a phone call from one of Audible's lawyers saying that if I want to continue as a customer I would have to sign an agreement not to mention this in the forum again. I signed the agreement and didn't mention it again. My account continued normally. I was never asked to stop doing it, only not to mention it in the forum.
In personal emails with that lawyer later I asked about that and she said their main concern wasn't that people might do that but that publishers might become leery of them as a source of piracy.
This was well before Amazon bought Audible so there's no reason to think they both have the same view of this but it's likely they do and so far Amazon hasn't taken many steps to make DRM removal difficult. It's a very safe bet they know all about it. My guess is they just don't care as long as it isn't a threat to their relationship with publishers.
You never know how things will change but at present I don't see any reason to think this is a hostile move on the part of Amazon. I sure do hope I'm right.
Barry