So all of the maps other than Mainland aren't possible in Absolute Minimum without a couple of changes.

1) Island is not possible to complete, as starting with only a Sand never gives you access to food. You wouldn't even be able to leave because the food check for using the Rowboat would kill the villager before you could. You would just need to add 1 Jungle to the Absolute minimum start to make it possible. If you also want to allow for completion of the Cathedral and associated quest/bossfight, you would also need to spawn a Cave. Spawning 1 Fishing Spot would allow for some other quests to be completed, but isn't strictly necessary, you can just never get fish. You'd just have to know not to fish there since you need to make a Fish Trap with it.

2) Curse of Death would be possible by adding 1 Graveyard, but it would be a very hard race against time without a bit of luck with chests/wood/etc. You do get given a second villager, so you just need access to Wood before the first one dies of old age. The Graveyard has a pretty good chance of giving you Soil, which would solve food problems as long as you keep at least 1 Plant of some kind around. You could also add a House if you wanted to alleviate the time/RNG pressure, but I suppose it isn't strictly necessary.

3) Curse of Sadness would require a source of food more than one single cow to be possible. A Cow produces 1 Milk every 90 seconds, and Long Days are 180 seconds long, so one(and maybe two, depending on timing) villager(s) will always starve, meaning it's not possible as you need three to craft a Euphoria. Adding a Graveyard would also make Sadness possible if you wanted to use the same trick twice. Theoretically, you can manipulate Sadness to spawn mobs to get food, but it would be extraordinarily unreliable with your single starting Cat. Also contemplating a Coin to get the 1 Happiness required to NOT spawn a monster every night would take up the vast majority of a day, as a cat 'crafts' 2x slower than a villager, and contemplating a coin takes(iirc) 60 seconds. So 120 seconds of your 180-second day would just be spent contemplating coins with the starting cat, which might make it into a death spiral if you can't kill monsters/get food/etc with the other 60 seconds left in the day, or if you lose too much health fighting them and can't catch up(since with no drops you can't get more coins so more monsters spawn, etc). If your Cat can survive(a big if), more Villagers join, but you would run into the food problem that would make the scenario impossible.

4) Curse of Greed is also impossible. The Royal when made Angry hits too hard/fast to be beatable even with the combat exploit. You would need access to other resources to get/craft Equipment + more than a single villager to be able to beat him if you don't do his requests. Again, a Graveyard would fix this. A Villager shows up later on to join you, so as long as your starting villager survives, and you can get wood out of chests, you could build a house to get more.

5) Even Mainland is "possible" but barely, as you can never get a second villager(since your second always comes from a pack). However, if you add a Jungle to Island, the one villager just needs to survive long enough to go there and search the Jungle until they get a Baby(which you can then build a house so it'll grow up, since you can get wood from the Jungle).

I know that you've said that part of the 'point' is appreciating the bare minimum, but I still think it should be possible to complete all the maps to some degree. Mainland can be completed just via traveling merchant/chests(especially if you provide a second villager somehow) and by going to Island.

The various Curse maps could be made completable via the things mentioned before.

TL;DR:
Add 1 Jungle to Island. If you want players to be able to get a Gold Quarry, also spawn 1 Gold Ore so they can construct one. If you want players to be able to get Fish, add 1 Fishing Spot.

Add 1 Graveyard to Curse of Death.

Add <Some Source of Food> to Curse of Sadness. Or 1 Graveyard. Food would allow the 3 given villagers to survive, and a Graveyard would let you get more food too.

Add 1 Graveyard(or some other means to get at least wood) to Curse of Greed.

I would also suggest adding some Soil to Mainland, so it's more possible to grow more food instead of relying on a 1% chance of a Rabbit from your first Berry bush. Otherwise, you would have to restart Absolute Minimum until you get a Rabbit from your first bush. Or just spawn them with a Rabbit to begin with to prevent grinding/resetting. Or a Graveyard(kind of an OP item now that I think about it, with how much it gives you access to).

About second villager on mainland: strange portals after moon 25 iirc spawn wolfs which can be tamed. You can then kill them for a graveyard.
About island: you can use double glue to send way more then just one villager to the island. See https://docs.google.com/document/d/1_2sMN2NsjX3RBoCY7B9FyKsEjtl6IBv7B2tqTK2FAHQ/edit#heading=h.9jomjgjboq5q

And, please before suggesting changes try to crack the puzzle for like a week. I know that when something is in development it's not clear what is intentional and what is a bug. But I want your initial assumption to be that everything is intentional.

I don't really know what you mean by "try to crack the puzzle" because, if you wanted to be more strict about a second villager on mainland(rather than a wolf/cat which are not guaranteed) then as long as you get to a point where you can craft an altar and get a mage, you can then do the challenge worlds.

And the issue overall isn't about "crack the puzzle" because without using exploits, the Island is impossible to the point that you can't even get your villager back home because they'll just die. There's no 'puzzle' to crack for the challenge worlds, either, they just aren't possible.

But the point still stands(which you haven't addressed any time I've brought it up) that the Cursed Worlds *are not possible*. If you want them to be possible you have to make some changes.

And I don't genuinely think that using an exploit to do completely unintended strats should be the answer to a problem in the game if the game itself HAS answers. Just feels unfair for people who want to play the game 'fairly'.

Bare is fair Absolute.
In absolute the whole idea of it is that it's impossible. It's not about having fun, it's about conquering the impossible challenge.
Kinda like Any Radiance mod of Hollow Knight.

I've managed to beat everything except curse of death using debug as RNG manip so I could try out more combos in less time. I do wish there was a treasure map on the island so I could put a relic in my cathedral, though.

And I just straight-up have no idea what to do about curse of death. I can't find anything in the wiki or on the link you provided that gets me more villagers from any combination of grape vine + 2 villagers + rabbit. Still, the puzzle solving was loads of fun!