My father-in-law is very sick and has dementia, but refuses to go to long term care. What do we do?

I'm hoping for some advice from anyone who has had to move a love one into long-term care against their own wishes.
My husband and I have been caring for my 83-year-old FIL for the past 2 years. He has moderate dementia that seems to wax and wane, chronic pain, and is wasting away due to having no appetite. He's about 105 lbs. We have not as yet found any evidence of cancer, but he is very ill. He speaks no English and has had no schooling past grade 1, and is functionally illiterate. He lives alone.
We live close by, and are trying to attend to all of his needs. He has gradually deteriorated to the point of not being able to dress himself properly, needing assistance with bathing, toileting, and cooking. He is basically totally dependent on others. We have 1 hr of PSW care per day, recently increased to 2. He is alone 90% of the time, which is no longer safe. He has had several falls and the PSWs have found him on the floor. He has also become totally incontinent, and on a daily basis I have to clean up urine and feces in all the wrong places--bed, floor, carpet...
We had a capacity assessment done through CCAC a few months ago to try to get him to apply for long term care, at least to get on a waiting list. It happened to be on one of his most lucid days. He is completely and totally against leaving his apartment, and he has told us several times that if we ever put him into a home he will kill himself. He's always had the tendency to be unreasonable, but of course his dementia has amplified this trait. In the end the worker determined that he was capable of making his own decisions, and said we could not apply to long term care, although we told her that some of what he told her in the assessment was not true (i.e., he said he would hire someone privately to care for him at home--he is on OAS and CPP and has no savings. He would not in fact be able to afford to hire anyone). She said that we could conduct another capacity assessment in 3 months.
The past 3 months have been extremely difficult for us, and for him, and he has greatly deteriorated. Last week we finally called an ambulance, as he had grown so weak he could not even sit up, and he began sleeping 20+ hours a day. He is currently in hospital being treated with antibiotics for yet another UTI. His dementia has progressed quite a bit, but he still has some somewhat lucid days.
We are involving the hospital social worker and are hoping to have a functional assessment done in hospital so he can hopefully be moved directly to long term care. The hospital staff we've spoken to have agreed that this is the best course of action, as he's not even able to stand up or walk unassisted now. However, we still need to have a capacity assessment, and we are sure he will never agree to go into long term care no matter how sick he is. My husband is the POA. We will end up having to move him against his will, and we are struggling with some feelings of guilt. We never wanted him to end up in a nursing home, but his needs have advanced beyond what we & home care can provide, and at this point his safety, rather than his wishes, is what is most important. But we know that he will feel betrayed and will never forgive us for making him leave his home.
Has anyone been in a similar position of needing to conduct a capactiy assessment to be able to move a loved one to long term care against their will?
I would really appreciate any input. Thanks, Maggie.