I would look into doing a first at $766,500 and backing it up with a small HELOC to make up the difference.  

I would talk to a Mortgage Broker on different loan types that would be beneficial.

If you live in California and have found your experience to be similar or different from mine I would love to hear it!

With a 50,000 difference your property may be a deal worth doing, but you need to know the numbers.

First, clearly outline your short and long-term objectives, evaluate your financial preparedness, and explore different investment opportunities.

Can I get an independent umbrella policy through a different company?

As Chris mentioned it works the same, however, the tax credits and incentives may be different for a primary home vs a rental.

But when you say the deal isn't as attractive, how much of a difference in the numbers are you talking about?

75%LTV + 15% seller but still 10% down so not much different than what Erik said besides 5% seller difference.Asking the good questions, as there are creative options out there! 

From most OOS investors I am speaking to this is where most of the attention is, so be prepared for competition - seems that this forum was revived from the dead but to answer the original question with a few practices you can manage the air-bnb yourself to get higher occupancy, I would recommend educating yourself on tricks for the platform those will make the biggest difference - definitely helps having someone take care of your air-bnb account and for completely hands off investing do that but just previewing/welcoming who comes in can be done remotely in a professional manner I have seen it done in multiple states.