I'm glad you got a response from Nitram and hope you'll get further clarification on the assessments.
I somehow suspected you were it in terms of family. For what it's worth, I am also an only child (as is my mother) so I go it alone with her care, although I do have support from my amazing husband. There is a childless aunt on the other side of the family, with mental and physical health issues, and I will be first in line (and possibly last) to deal with her, if and when something happens to her current carer (my other aunt, her sister). I get a lot of sympathetic noises about the only child situation (poor you, bet you wish you had brothers and sisters to help you) but it's not as if I can do anything about it. Also, interestingly enough, I've been an only child all my life and so long ago came to terms with the idea that it's just me. My husband, on the other hand, is one of five children and I dread the day that we have to deal with a crisis with one of his parents; one of the siblings is semi-estranged and all five of them together couldn't decide on what to put on a pizza, let alone make emotionally wrought health care decisions.
But I digress; for which, my apologies.
I did try not to sound judgmental and say that the situation is ridiculous; I do not wish to be offensive. Certainly your mother is hardly the only older adult to wish to be independent, not accept help, not want to embrace change, et cetera. Any amount of time on TP and/or in carers' support groups has taught me that, as has the experience with my mother.
Having said that, and for what it's worth, no, the current situation can't continue indefinitely, as you note. Something has to change and/or you will have to wait for the crisis.
Here are some strategies I've seen outlined here on TP, and heard elsewhere, in terms of persuading reluctant family members to accept help:
-first, always be aware of not just the message, but the messenger. I had a brilliant carers' workshop where we were taught this very thing. Unfortunately, the adult child is almost always the worst messenger. If you can get someone else to deliver the message, do so. Suggestions include: other family member (clearly not going to happen in your case), health care worker, social worker, doctor, clergy person, neighbor, basically anybody but you.
-if that won't work, and even if it does, remember to shift blame wherever possible. I find blaming the doctor or hospital works best (Mother, I know you don't want to go to that appointment; however, the doctor says you must) but your experience may vary.
-as your mother is not the one with dementia, consider a personal appeal. Tell her you understand she doesn't want help/a cleaner/strangers in the house, but that you live far away and can't do it all yourself, and it will help you if she will accept them coming in. Sometimes a parent will be willing to do something they don't want to, if it's framed as helping their adult child, rather than themselves. Some people find this approach can even work with the PWD (person with dementia), but of course it's impossible to predict.
-some PWD will accept outside help and "strangers" coming in, if they are framed in a different way. Approaches I've read about here include: this is my friend Mary, mum, and then in an aside, she needs the extra money dreadfully, Mum, so if you'd just let her work here a few hours a week it would really be a kindness; this is a free trial service from the council/NHS/church/community centre; this is a student who needs experience to get her degree/certificate so could you please help her out.
No idea if any of that will work, but thought I'd put it out there.
I'm very relieved to hear you have Power of Attorney sorted. Here in the States, you can't get anything done without it (and often seems you can't, even with it!).
It also sounds like you've done a lot of work already. As someone who was formerly a long-distance carer, it's an awful job under any circumstances and the distance makes it that much harder, and puts a lot of miles on the car!
I'm just so sorry about the difficult circumstances. If you're inclined, I hope you will keep us posted, please.