My plan is to use the extra $1000 to build up a 3 - 6 month emergency fund, then build up my 401k and other investments. 

What you should do is let them all know you will only respond to non emergency situations between 9am-5pm Monday - Friday or something of that nature.

They'll probably stay a few years or longer,probably won't trash the house when they leave, maybe you hire a prop manager and outside of an emergency you don't do that much.

I’ve gotten half the usual number of applicants on two of my rentals for 2018 as in the previous 5 years on average.So much for our “emergency housing crisis”

Materials can be easily quoted, but it is the labor that can be shady along with a mark up for, "incase of emergencies."  

Both of these loan programs can get you into a home with as little as 3% down, which would give you some additional capital/reserves for improvements after purchase, or a larger contingency/emergency fund, or a good place to start on your next home. 

My wife and I keep most of our money in Ally for the interest rates but we want a local bank to keep emergency cash in, get cashier's checks from, etc. 

Plenty of different methods to save up for a DP and establish a emergency fund.

It is within driving distance for you, which can be very helpful if you want to check on the property, if you have an emergency or if you are planning on using the property occasionally yourself (which most people do, it's a great perk of owning a home on the beach).

Using a cash advance to purchase might be okay if you have the funds or at least some of the funds and can pay off the loan immediately in an emergency, but I think it's a terrible idea and a recipe for disaster if there are no emergency funds available and you can't get financing or even afford insurance.