Our insurance has been canceled on this home and we are working on getting insurance to cover when this current one ends.

It's a small place so I'd guess it won't rent for enough to cover your expenses anyway so I'd probably sell, especially if the loss is small, it unless it's in a great neighborhood that you think will do well over time. 

Real numbers- purchase 907k,rehab , closing costs, soft costs, 840k, all in 1.747 mil, basis for each unit should be roughly 291kappraisal of each unit minimum 400k , so 2.4 mil if for all 6.I might refi only 4 out of 6, that will cover initial loan amount.

At this point, I would recommend having a line of credit to cover these things so you don't have money sitting in the bank doing nothing when it could be put to work.I have 33 units, no debt except for mortgages, and excellent income.

We like the short-term rental idea because we could stay at the property ourselves when we want - summer break, spring/winter breaks, etc.Our budget will be right around $1M or less ideally, and we would like a short distance to the ocean.How likely is it that we could find a property as described above and have it cover or come close to covering the mortgage? 

The least states:"Tenant shall pay a "late charge" not in excess of five (5%) percent of the amount in arrears for each month the arrears remain unpaid if any Rent is paid more than ten (10) days after the due date thereof, to cover the extra expense involved in handling delinquent payments.

I suspect I will throw more money at a problem Airbnb has no interest in covering

Their clear incentive is to bet on falling interest rates between now and debt maturity.A small handful of owners are forced to sell due to a looming balloon payment that a refi won't cover, but you're not going to find one of those by driving the market when any commercial broker can just look up properties on that basis and start making calls. 

We have done it both ways where we fund purchase and they cover rehab but if the individual is less experienced we do not do it that way, we have them put more money into the deal from the start and fund the draws, reason why is we also had a deal where the person said they would do this and never did anything and property sat and loan matured and it was a pain.Just recognize you will still not get 100% financing for the purchase, so you are putting money in up front. 

More than enough to cover the check written on the undisclosed transaction account.