How about a live-in nurse? Like a live-in maid but only for nurse related stuff. Get one of those working for $10, up their pay, and hire them personally or through an llc if necessary. I don't know if such setup is done here but in other countries is not uncommon. As an employer you control everything, you just got to be fair in terms of hours, what responsibilities, times, days off etc.
Nurse end up earning way more and you might even spend less than in a home by cutting out the middleman if you structure it right. If you do end up paying more it might be worth it to create a much better environment. I'm not a fan of old people home in general.