I got the distinct impression from the agent that it was the bank holding  things up (including the price,) as much earlier in the process they'd had an offer accepted by the bank, but because they dragged it out so long, the offer maker withdrew. 

I do stove and fridge (no ice makers). 

If you live close enough to your property or have a friend or relative nearby, a drive by can be helpful in alerting you of any issues; for example, unauthorized cars in the driveway, debris, garbage or indoor furnishings outside the unit, etc.I think rental owners who don't require their managers to do regular inspections or who fail to regularly check up on their properties are the ones who are more liable to property damage because they probably don't screen their tenants well either.

It's better for you since you won't have to worry month to month whether she'll be able to make rent and you won't have to go through evicting her.  

We still put microwaves in them.No water/ice makers in fridges.  

While it is a temperate climate, it would still get pretty hot indoors without any windows open.I should also note that we once lived in a small condo here (less than 800 sq.ft., and bought a window A/C to use a few hours before bedtime and during the hottest hours of the day.

When you start trying to justify or explain or rationalize what they might really mean - when on the face of it, it doesn't make rational sense - deny!

I would include a question: "Are any applicants indoor smokers?"

They are still behind a month and change.It's become blatantly clear now over the last couple of days that they are not getting out of their hole anytime soon ($1200 water bill they have not paid in 9 months and have been cut off...) and they will make rent the last priority.

Having the HOA change the bylaws to make renting more difficult or impossible is a substanial risk without possible mitigation.