So sorry, this must be very difficult for you. The support and help of a family nearby can only be a good thing. It would give you a break too which undoubtedly you will need and deserve. However, at the end of the day, only you can decide.
Some areas have I.D. bracelets that related to a photo on record with the local police (in case he's found and needs help being brought home). A GPS gadget (there are watches that have this function and are trackable, now might not be too early to contemplate gifting him with one). It ought to be reassuring that if he did go missing, there'd be a way to track him down.
If he has high anxiety levels during testing, his (Mini-Mental) MMI scores may be meaningless. I mean, I suffer from anxiety myself at times and if it's under poor control I'd flunk an MMI test no matter how hard I tried (my parents went through several of those tests, so I'm quite familiar with their content and application). Perhaps the test(s) ought to be retaken when his anxiety's well under control, even if he needs to be medicated (eg. some serax/oxazepm for that purpose).
A small town would not have much in resources, perhaps your larger area has: a daycare center, a seniors assisted living facility, and of course, rest homes for those completely unable to care for themselves (some have specific designs that cope with alzheimers' patients propensity to wander), though I think the latter vary widely in quality and safety.