Weird idea, but what if there is a cumflation mechanic where Rina could use her womb/anus to hold excess cum to replenish her mana? Perhaps other means of obtaining mana could be blocked or nerfed, like reducing the effectiveness sleeping or making mana potions ludicrously expensive to make the cumflation mechanic more valuable? The game Dryad Quest comes to mind here but instead of using cum directly she will need to "absorb" it first.
Regarding pregnancy, I kinda agree with you that a baby-making machine without any attachment to the child or monster spawn kinda lacks appeal. However I kinda disagree about making it story-bound or GOR-only. I tend to prefer systems where menstruation cycles and sperm availability ties into pregnancy .The uncertainty and risk kinda makes it more kinky as opposed to more predictable events. Heck we could even get dialogue about her worrying about pregnancy every time she gets creampied when ovulating.
Regarding child/spawn attachment... perhaps a nest-based mechanic of some kind could be created where Rina would try to to manage her own nest of monsters with a population cap of some sort (5 or 10 monsters)? And Rina will have to manage the relationship with her spawns... like make them more attached or in love with her (perhaps you could even tie in some story beats into this?).
The nest could also serve to function as a means of collecting more cum/mana that ties in to the proposed cumflation mechanic. If you think adding a crafting mechanic to the game makes sense, you could even have them collect crafting resources or something when the relationship with her spawn is higher.
Not sure how much of the story you have fleshed out already, but... one thing that seriously appeals to me is monster pacification. For instance, perhaps Rina could (after significant story beats and character development) consider it her duty as a soldier to maintain the peace between humans and monsters as opposed to exterminating the monsters. Of course she maintains the peace sexually