Hello Jachro,
I also have worked as a caregiver in LTC and home care. I also identify with you in that I decided to retire early to take on helping care for a special needs family member.
so far as I know there is no compensation available for family members helping out at home.
i wish there was, as it is a full time job being a caregiver - for family member, spouse or whomever.
caregiving isn't cheap as you know, but finding the way to do it yourself and be compensated is going to be difficult. Notice I didn't say impossible. Sometimes there are exceptions to rules.
i hope that someone will be able to give you some better options than I can.
i wish you the best and admire you for your commitment to your father, and hope that maybe you will be able to find a solution - even if it is not what you and your dad would like.
If you can persuade him to take a bed in a nearby facility / it means you can visit and support him - and yet still support yourself.
Best wishes,
NatR