I have to very much agree with your assessment there, RNG based gameplay in a story / smut based game generally just leads to frustration (and not the fun kinky kind). If you want to keep the idea of having to do multiple playthroughs to see all content, and encourage replaying the story in different ways, my suggestion would be to make it more of a limited branching system, where the player can pick freely from a set of options each time.
So something like this for example (bold is what the hypothetical player picks):
1st Recruitment mission selection
* Recruit Estallar
* Recruit Helyra
* Recruit Xotyli
1st Regular guild mission selection
* Rat Quest
* Noble Quest
* Quest A
2nd Regular guild mission selection, last time they picked Noble Quest so there's a new option
* Rat Quest
* Quest A
* Quest B
2nd Recruitment mission, last time they recruited Xotyli, so only two options left
* Recruit Estallar
* Recruit Helyra
3rd Regular guild mission, the player didn't accept the rat quest within a set amount of time, so someone else solved the problem instead. During next round of regular guild missions B will be removed as well if not picked.
* Quest B
* Quest C
* Quest D
