SleepTown (which we got on Android via Google Play) tries to encourage consistent sleep cycles in a Recycling Digital Motivation Suck as Leverage way. It accepts manual trigger inputs when you sleep and wake within −2h ≤ ΔT ≤ 10m of a target time. It also locks out the rest of your handset functions when you're supposedly asleep, to try to prevent “pick up handset in the middle of the night, read terrible shitposts for hours, oops, the light from the screen and the infinite cat videos kept me up, now everything is ruined”.
When you trigger a cycle while going to sleep on time, it begins “constructing a building”. If you wake up on time (possibly triggered by the builtin alarm clock), then the building is revealed and added to your town, and you get coins based on the total number of buildings you've successfully constructed so far, plus a bonus based on consecutive successful days. If you oversleep, or if you override the app switch lockout, you get an unpleasant-looking broken building added instead. Enough successful days in a row without a failed one will get you a “ticket” which you can spend to increase the chance of rarer buildings. Coins can be spent on rerolling construction results, demolishing failed buildings, or decorations (see below).
Much like Forest by the same company, it's “free” as in “demo”, with the real thing being a 2 USD in-app purchase in the Settings menu.
The tuning on this one is much more awkward than Forest. There's no way to explicitly fail in the middle of a cycle except by triggering it noticing an app switch and then choosing the option to destroy your building. The chance of having an actual need for some other app during the much longer contiguous lockout period is also higher. The builtin alarm's vibrate-off setting doesn't seem to work (which we should see if we can report to them properly at some point). Not triggering a cycle doesn't count as a streak failure for the purpose of tickets, which is understandable given there's no support for inherently variable sleep cycles, but feels odd. Also, changing your target times resets your streak, which is also understandable given the purpose of the thing, but it's also why we haven't gotten any tickets at all yet (except for possible a single one that you get as a starter). >..<
Aside from the main “big” town (which is populated with your buildings in some arbitrary fashion), you can build your own maps out of the buildings you've picked up, plus decorations which you buy with coins. I haven't really dug into that part yet, though it looks neat. A different thing I have tried and like is the “shaking challenge”, intended to make it awkward to reach up, push the wake button, and then instantly drop back into bed, by giving you a bar that you have to fill by shaking your handset before it'll believe you're actually awake; if you stop, the bar gradually drops back to zero. So that's kind of a nice physical trigger.
Overall I'm more ambivalent about this than about Forest, especially for us specifically, given distinguishing between “unwanted inconsistency” and “our sleep cycle is requisitely getting jostled around and we should just roll with it if at all possible” is tricky. But during times when we are intending to be consistent, it's kinda useful.