Thanks for getting back to me. You’ve prompted me to have another look at Plex (which I already use), and it turns out Photos have several of the features I’m looking for. It’s possible to use the remote control to switch between random and sequential, and from a random photo, it’s possible to switch to “On this day”.
The major thing missing is making this available as a screensaver on the Roku, so that it activates automatically after a set idle time. Currently I have to enter the Plex app and navigate to Photos in order to start the slideshow, which in practice means I’ll look at my photos only occasionally, rather than daily.
I’ll see how far I get trying to lobby Plex to add these missing features. E.g. they can easily add “In this month” and “In this year” in addition to “On this day”. Since my photos do contain EXIF keywords (names, places), it would be great if I could select those too, but I have less hope of that.
I did try Chromecast’s photo screensaver, but it didn’t have the features I list above. It also felt silly and wasteful, even with unmetered bandwidth, to be forced to pull my photos off Google’s servers rather than my NAS in the same house.
I’ve used Google Photos quite a bit, and I’m impressed and frustrated by it in equal measure. The content recognition AI is amazing just as often for what it is able to recognise, as for what it somehow fails to. As a lifelong photo organiser and album creator, I’m unconvinced by relying entirely on algorithmic photo organising, and I find Google Photos ignoring my tags, albums and folders, and killing off perfectly good software in Picasa, hubristic and infuriating. I also find the Google Photos UI a classic case of over-simplification, in which Google is a major offender nowadays.
Anyway, thanks very much for getting me further in my search!