How to find placement for Dad?

Dad is mid 90’s and has lived in my home with myself and my husband for five and a half years. My husband will listen for him on the rare occasion that I go out, but rightly does no hands on caregiving. I am “it”. Dad has many chronic health issues and all five senses are greatly diminished, effecting daily life and ability. Mobility and balance is low/considered a high fall risk. Walker around the house (he sticks mostly to “his” area of the house and the big covered porch outside his room now), wheelchair most everywhere else at this point. A fall about two weeks ago with no fractures, but pain and some other things, resulted in his becoming increasingly sedentary (pain in lower back) and is now struggling to stand. Constant vigilance day and night is necessary to ensure safety. That being said, he is insistent on doing things for himself, but increasingly is needing help with ADLs . He sleeps much of the time (but then is up and down during the night) I am so tired that I don’t always hear him now, which is a worry and safety issue (I do wake up frequently to check on him). He has had cognitive decline in the past six months or so that is very evident off and on and increasingly more noticeable now.
In a nutshell, he is declining and may soon need physical help that I cannot give due to a health issue I have that precludes heavy lifting, and because I can’t stay awake 24/7. In home help is not accessible—no one wants to risk exposure to infectious disease he has had off and on.
I have been looking at area nursing homes and am having a hard time finding one I feel good about, but know no where is perfect. . Also, it seems like direct admittance without the hospital stay will be difficult. And with his type of insurance, and what he is usually hospitalized for (infectious stuff requiring a private room, or needing IV antibiotics that skilled nursing doesn’t want to accept because of cost with low reimbursement), no one would accept him post hospital in the past. I am looking at them (touring, looking up inspection reports and reviews, etc), with idea that we could try direct admit now while those obstacles are not part of the deal—but if it doesn’t work, try private pay post hospital? He has enough to be able to pay, I think, for about a year and then would have to do Medicaid. I also have to get help planning for that, as I do not think he qualifies.
I feel anguished at planning this. But the stress of daily care and having little to no freedom for many years is becoming overwhelming. And, I have had a taste these past two weeks post fall, of what life could easily devolve to—and it is not sustainable. And my sweet husband has finally had enough and insists that I find alternative arrangements for dad’s care (he is a compassionate man but it’s been a lot of years, even before dad coming to live with us, of little and now no freedom, supporting my parents physically and financially for a very long time. It’s ’more than my husband’s turn now that he is newly retired. )
Any suggestions for achieving placement in a reliable facility would be welcome. Also, how to broach subject with Dad when time comes…(Early on we did talk about this possibility someday—I just doubt he will recognize that someday is now).