What strategy would you suggest I follow instead?

As I suggested and you confirmed, the Côte d'Azur is a great place for capital gains but what I meant isn't necessarily where you're going to get high rental yields.What @Chris Magistrado mentioned represents a good depiction of the situation in Southern Italy.

Fortunately our remedy was fairly simple, large floor fans and new ceiling tiles but it was a massive inconvenience and the damage would likely be much worse if it repeated in units in other places.

As easy as this sounds, it's not simple and usually like pulling teeth.

Agree with others that you will probably need to lower the rent - suggest 5% every 2-4 weeks until activity picks up. 

Simple.

I work on projects across multiple states and have a strong network of contractors.Regarding when to involve a contractor, if it’s someone you haven’t worked with before, I’d suggest waiting until after the inspection.

Very good point.In the case of Arizona, I have been unable to locate any state law / code that suggests Arizona may have additional regulations. 

My current agent suggested if it made sense financially, to do some rehab work to get the properties rent-ready, but I do not have the liquid funds to do so and sell these as-is.

I highly suggest you go.And it's VEGAS!!!