I recently came accross Lisa Mona thanks to this video: https://www.youtube.com/watch?v=rthNKvnWEvs&t=217s
I didn't actually play it but it is presented as a "randomized puzzle roguelike". Maybe not exactly what you are asking for but here you are.
I feel like a rogue-like version of the civilization genre could work.
What I mean is:
The latter is needed because the former means you would play many more games. So they have to feel different.
To make games shorter you would probably have to remove any tactical combat. Maybe just say "attack here" and the game automatically sends troops for you, battle it out and shows you the result, in a few seconds. Maybe you can see the battle itself but not play it. Not having to move units on the map should also make the IA play faster and thus reduce waiting time between turns significantly.
To compensate for the lack of depth in combat, city building, building your economy, and random events would have to be made more interesting. Without introducing micro-management that would make the games more tedious and thus take longer.
To make games feel different with randomness, a fantasy setting seems ideal, like in age of wonders. Tons of fun stuff can happen when magic is involved. Focus on telling a story.
Basically I love the fantasy 4X genre but I find the games too long for the wrong reasons (too much micro-management and tedium). Bringing in ideas from the modern rogue-like genre could help fix those issues.