I'm an older people's psychiatrist
Delirium can't be treated as such although the causes of delirium eg infections, medications, etc can be.
Sounds like he's had a very bad time with 3 separate infections. The sicker someone is physically the worse the delirium and the longer it takes to clear. Often 6-8 weeks. They may not get all the way back to baseline and sadly (not trying to scaremonger) some people die and for some it does uncover underlying dementia.
What he needs now is time, good nursing care, good nutrition and hydration whilst he recovers rather than more treatment.
Honestly he may well be better in a care home than a hospital. In hospital people pick up all kinds of nasty resistant bugs, everyone is very sick, machines beeping all the time etc. It's a scary environment if you are confused anyway.
If you find a good nursing home with well trained staff he will be well looked after and might recover better. He can have community physio at a care home when he's mentally well enough .
It doesn't have to be forever. You can sign a respite contract for any period of time eg 6 weeks and after that he may be well enough to come back home.
If he is paying privately care homes will be keen to accept him as they can charge higher fees. This may seem unfair but you get what you pay for in the world of care.
I really would look at as many as you can. Meet the manager, look around, check how the place looks and smells, see a menu, see how staff interact with people, ask how they would help him recover. Some care homes specialise in rehab these days.
Don't look on it as writing him off just the next step in him recovering.