Empath trying to cope with emotions: long distance caregiving of dad for Parkinson's. Advice?

I'm one of those 'highly sensitive' people - an empath who absorbs others' stress and energy, to the point of my own depletion. I try to limit exposure to things that stress me out, though the pandemic and social crises of the last few years have not helped. The primary problem: my widowed 93 year old father lives alone, 3000 miles away. We kids are all on the west coast, and he's on the east coast. He's always been a very difficult person; overly critical, irritable, self-centered and doesn't recognize that people, especially family members, are separate entities with different opinions and boundaries. (He does have good qualities but the negative ones stand out the most to his family.)
Anyway, he developed Parkinson's about 5 years ago, and his memory problems are getting worse. He passed his mini-mental at the neurologist's recently with flying colors, though I realize people can pull themselves together when they are to be tested. I'd say he's 'himself' about 75 percent of the time, but his short term memory is awful; he can call several times a day without remembering that he did. And he has episodes of paranoia and occasional visual and auditory hallucinations.
Because I am the "nice" kid in my family, a long-recovering "good girl," he leans on me more than the others. In life, I am a dogged problem-solver, too much so - I realize it's a way to control my anxiety about things. His needs over the years have grown exponentially, with constant long-distance computer, phone and TV troubleshooting, plus a 'short' conversation takes 30-60 min because he won't wear his hearing aids, and thinks and expresses himself so slowly. We sibs share some of the troubleshooting, but he calls me more because even though I work full time, I'm easier to reach and more emotionally 'available' to him. I do set limits - but as he gets more forgetful, they don't work well. (I've said "I can't chat during the week, just on weekends.") Some people might say 'just block his number' but I don't feel I can turn my back on him like that. If I don't return calls, he texts repeatedly in a mild sort of panic. I often ignore it but it keeps up.
The secondary problem is that we've been trying to get him some in-home practical help so he's not calling us all the time. But - bet you can guess - he won't hear of it. He has a grocery shopper and house cleaner for now, a younger friend, though he may lose her soon. We've been trying to get him to move to where we live, and he pretends that he wants to, but refuses to let anyone else help sort through his house with 50 years of belongings. He must look at every piece of paper and ancient travel brochure, decades of old stuff. It takes him a week or two just to go through one box. He thinks he wants to rent his house out if he comes to live here. It needs to be "empty" he says. He won't entertain any notion of locking up the place, and leaving it for us kids to deal with after he's gone. He obsesses that we'll throw out some important papers... like a work letter of commendation he got 40 years ago. We promise we won't do that (fibbing), but he still won't budge. He'll let us help only if he supervises. (But we don't live there, and can't come enough to really speed this 'move prep' up. )
I've been looking at assisted living places with an eventual transition to memory care on the chance he does make it out west with us. But, his planning and executive function/thinking is not good, so we all just go in circles. It's gotten excruciating and something has to give. It's starting to be me. He's fallen several times in the last few years, so far no real damage but that's not going to last. (He's also had metastasized prostate cancer for the last 2 years. But he just keeps on rolling along. ) I'm really concerned about my stress levels; they've been elevated most of my life from being sensitive, and I just don't want this anymore. None of us can really do any more than we already are. Thanks for listening! It