Except, that's not really what I want to do either.

Then you have a problem

I recall one game where die for reward was OK, it was a small game where you descended to hell and was dying and getting stronger while traversing it. It was thematic, it made sense there. But... I pretty sure it's not the kind of game *YOU* wanted to make

Get rid of the "die" part, rename it, rebrand it, hide it, whatever. It's not compatibe with the mood you are after.
Also, you are a breeding freak, so why not go somewhere that route (going after ones strengths is always a smart move when designing, at least to my experience)? Make some generations, older ones retire and new ones take place. The young build on the old and are better because of the ancestors.

Death doesn't have to be a serious thing, there could probably be a take on death compatible with any mood. But ok, what is the mood I'm after?

I want the main character to be in possession of secret knowledge of the future compared to NPC rivals. I want the player to be becoming wise, in the sense of learning how to exert a small amount of force at a key point to cause a large affect, and to solve problems not by attacking them head-on, but by subtly in advance knocking them off course. I want the player to be in the position of taking actions which are important to the future but seemingly nonsensical to the NPCs around them, thus creating additional difficulty for the experienced player by lowering the main character's relationship with those NPCs because they think the main character is weird or crazy or suspicious. The player should at first be exploring the world to learn about it, then using their knowledge to hypothesize a strategy for manipulating the world to progress toward a better outcome, then test their strategy and revise as the different actions of the second attempt reveal new information and options. The ultimate goal is to get to a perfect ending. One goal of the game design is to create a small setting and relatively small cast of characters which can react with tremendous, intelligent flexibility to the player's actions. This is something I feel is direly lacking in most games which have a replay mechanic.

I'm undecided about whether I also want the player to be making their main character perfect in terms of physical stats, combat abilities, wealth and possessions (i.e. a base like mentioned by TechnoGoth). Theoretically this game wouldn't actually have to have combat, but I don't know what else the player would be doing to as their "daily work" to earn progress. I do really like the kind of game where the player starts out at the bottom of the pecking order and works their way up, gaining recognition from NPCs, but I'm not sure it fits well with the time loop structure. With both ranks and wealth/possessions/a base, it would be challenging to find a way within the story for them to persist when the player resets the time loop. I definitely don't want the player to have to climb the same rank hierarchy every play-through.

Basically I've described a groundhog day time loop (and the main character did die several times in Groundhog Day, despite the movie being a romantic comedy). He didn't die _usefully_ but that's because the movie's theme wasn't about strategy or subtlety, it was about emotion and transcendence. The TVtropes wiki has several pages related to groundhog day, time loops, peggy sues, mental time travel, and that sort of thing. I went back to look at them again, since it had been a while. A few games were referenced as examples - Warthogs, which is a Harry Potter parody fangame in the style of an old hunt-the-pixel adventure game, and Grim Grimoire, a PS2 anime strategy game set at a magic academy. Warthogs I already downloaded and tried, but didn't like very much because it was hard to understand the base state of the game enough to try to make a change to it, and the few legitimately-interactable items were buried in fake ones. Grim Grimoire I added to my "games to possibly buy soon" list.

I always loved the groundhog day idea. My favourite take on it was the very funny episode of supernatural about the mystery spot where each day Dean dies in weird and wacky ways.

If you're looking for examples of games like the only one that spring to mind is Majora's Mask where you have three days to save the world. If you haven't managed to get everything in place to stop the moon from crashing into the town then you are sent back to the beginning. Its good because there different things happen at different times and the clock is always running and there is something you can do to help everyone one in town you just have to figure out what they need. You only need to help them once and that permanently solves their problem in most cases. They varied from listening to an old lady's story to stopping aliens from abducting a girls cows.

You don't need combat in time loop game to make it work. You could take elements from the life sim games like princess maker, long live the queen, magic academy, lifequest, and then throw in some mystery and relationship building elements.

The character could take art or cooking classes to improve those skills, get to know the people in the town and peice together their back story. Want the two brothers to reconcile? You need to back the cake their mom used to make and find the lost toy.