Bob,
I would take the letter as a positive. There are other people who care about him. In the three or so years when I knew there was a problem and was unable to do anything about it, I am sure that there were others who were concerned. What I am equally sure is that my mother did not let on that I was there and trying to help. It was if she could elicit more sympathy and support if she presented herself as alone and vulnerable.
When she had her fall a number of people appears quite surprised, and relieved, that I was around. This included bank staff, her church, her solicitor, building management, neighbours etc. I assume she was worried that if she told them about me and and vice versa we might all gang up on her.
I really understand this desperate fight to retain independence, but equally there comes a point when the dementia becomes so advanced that this fight is irrational and unsafe. What you know, and what the Church is telling you, is that point has probably been reached.
I would approach them and thank them for their concern which you share. Listen to what they have to say and note evidence of specific examples of unsafe behaviour. Also take advice. Vicars and priests do a lot of visiting the elderly and will have good ideas of suitable and local alternative accommodation. And/or how the system works in your dads area.
When I was clearing my mother's flat and preparing it for rental, I was able to tap into huge local goodwill, including reliable tradesmen. People were pleased to see that my mother was being taken care of and in return went out of their way to help me. Plus advice on all manner of things.
Then perhaps phone the GP, or ask for them to phone back on the basis that it is not just you who are worried but the church, neighbours etc. The agenda will be "is it time for the next step" and "how to get there given your dads reluctance to consider alternatives". You will need to throw in the need to find something for your brother.
For everything you have said it sounds if it needs to be done. And whatever the guilt think of the relief when you can answer the phone without wondering what the latest installment is. Plus your dad is probably very stressed, lonely and confused. Getting lost must have been terrifying. He could well be much happier in a suitable setting which allows for his disability but allow him company and scope the use his remaining faculties.