The best way to make the numbers work is to limit the work to cleaning, paint and carpet and avoid expensive projects like roof, windows, replacing plumbing and electrical systems, driveway etc - as these take huge amounts of capital, but will typically not drive up the ARV by much.

To limit your liability I would highly recommend you hire a property manager.

The loan limitations will be deed seasoning and your LTV max.

Lastly check your local landlord laws in the earlier scenario that you could command a higher rent basis will be shut down if your law limits the amount you can charge either by percentage or dollar amount per year.

You can bring additional cash to the table to purchase the replacement property, you’re not limited to the cash generated from the sale of the current property.

Are the deductibles and limits the same for each quote? 

@Suzanne Player Applecross limits the number of rentals in the development.

You could even work with a real estate agent and find properties that are listed (although this is very tough right now with limited inventory).   

Even with my powerful "why", I still do not know the process for managing an out-of-state investment with limited ability to travel. 

As your focus gets narrowed into an RV park, the risk increases, because if a project like this did not succeed, the number of buyers and demand for it as an REO would be very limited.