Have you considered adoption? Plenty of kids need good homes, and that would eliminate the possibility of any father ever laying more "claim" to the child than the other.
I hesitate to add this for fear of straying off topic, but it an oft-repeated misconception that there are "plenty of kids waiting to be adopted." This was true decades ago, but not today. While technically true in the strictest sense, there are huge waiting lists for children under age 5 that are not disabled. Parenting a disabled child or an older child (who almost certainly has endured major trauma to be available for adoption) is not for the faint of heart - and is not something that should be encouraged to any woman simply because her baby-making parts don't function well.
Anyone, regardless of the state of their reproductive system, who has the desire and capacity to care for such children should absolutely pursue that path (and if you're not sure, try fostering. There is, quite unfortunately, a world of difference between "normal" children and those that have suffered abuse and neglect). But requiring IVF to reproduce and being such a gifted person are two unrelated features.