Chris pointed me to an app he found - Arc.
I tried it out. Different interface to Moves. You get the timeline of events up front, overlayed on the map. It took me a little while to find how it worked. I should have read more. Beside the locations it found, and besides the transportation methods, I had a lot of little red dots. These mean it wasn't sure of these things. The more you use it, and the more you eliminate the little red dots, the more confident it gets in placing you and working out your movements.
When you start the app, you get the map at the top with your movements marked. Tap on the map and the other views disappear and you can move the map around, expand it and shrink it with the usual pinch and pull gestures. Tap the X at the bottom to go back to the main view.
You get a horizontal bar in the middle which summarises your movements. Tap on that and you get an expanded view of your activity.
Then you get your timeline in a big view at the bottom. Slide up and down to see it all. You can tap on segments to edit them, and correct the location and activity. There's quite a lot you can do there.
Right at the top is the date, and you get a calendar to move around. To the right of that is a double arrow to go to Today. If you just want to move around a day at a time, swipe left or right on your timeline.
At the bottom left is the Arc symbol again, tap that and you get the menu.
Top left is a search button, and I haven't done a lot with it. I searched for Acredale (the cat's vet), it showed me a lits of my visits there, let me choose one, and then showed me the timeline and map for that day. That's really nice.
Overall, it's an easy interface, and the more you use it, the easier it gets. I'm liking this app.
Once I started confirming and correcting things, I was in a better position. What I particularly like is that the data is stored in iCloud. It does not appear to be sent off the phone to the developer. I have the data, I control the data. I like that. It also seems to be lighter on the battery than Moves was. I also like that.
There have been several updates to the app recently. It's under constant development. The author announced that it might be possible to import Moves data. This morning, that update with the import came through.
The import method involves getting your data from the Moves website. It's in a file called moves_export.zip. You put that whole file in your iCloud drive, in the Arc App directory. Once you do that, you go into Arc and it should import your data. It didn't do that for me. I moved it into place on my Mac. When I looked at it on my phone using Files, it had the little iCloud symbol on the icon for the file. Ah, it was in iCloud, but had not been downloaded to the iPhone. That's why Arc hadn't started importing it. I tapped the icon, it downloaded to my iPhone, I went into Arc, tapped the little Arc symbol at bottom left, and it showed that it was importing my data. Nice.
It didn't take long. I have a lot of data since 2014. The iPhone ran pretty warm during the import. I did some spot checks on the 2016 Hawaii trip and the Pennsylvania trip, and the data was there. The locations, places, times, it was all there. My history has been preserved. It's viewable, and usable. This is awesome. Most of the imported data has the little red dots beside it in the timeline. I think I need to go through and confirm every entry. That's going to take some time. I also seem to have two different items now for Home and for Work. Not sure how to reconcile these different items with the same name.
The Arc app is free. But you can back the author. I sent $10 to the author last week as I started to use the app in earnest. After the import worked so well, I just sent another $10 as a thank you. This app is a great replacement for Moves.