My father is incontinent, has nephrostomy due to kidney failure, has serious mobility issues, heart attack, metastatic prostate cancer.
My mother has mobility issues, chronic afib and can't get around. They are both becoming confused especially my father.
My father is a veteran but we have had a lot of problems getting veteran benefits.
If they don't qualify for Medicaid, then perhaps hospice would be good. With his conditions, your father sounds like he may qualify for hospice. The potentially bad thing with hospice is that your father could not receive rehabilitative care, only palliative care. The good thing is that they will work for what Medicare will pay.
Please let us know how it goes for them. Many people are in the same position as you are. There are so many hard choices to make. None of them seem to be good choices. We just have to choose the one that seems best.
I'd start by contacting NH in your region to see which can work with you in doing the Aid & Attendance benefits and also takes Medicaid. Good luck.