Regardless, states other than NY also didn't prevent it getting in via staffers, visitors or delivery folks or however it got in there and have a similar, terrible LTC death toll.

As an engineer, if you gave me this problem, I'd secure every LTC home with 24hr police / national guard. All staff would be do 3 weeks on, 3 off, but while "on" (think oil rig workers), living on-site in trailers or [hm]otels, not going home every night (movies do this when filming on location; juries get sequestered for important trials, why can't we do this here?). When staff go on-shift, they must be isolated and then tested before being allowed to go onsite. Deliveries left on the loading dock and properly sanitized, and no visitors -- AT ALL. For Medical emergencies (local FD / EMTs), the resident & 1st responders would have to be isolated for triage, then taken off-site and go back through quarantine / testing to get back in.

It's totally doable and the cost is a heck of a lot less than an economic shutdown / lockdown, or the continued high death toll.