If there might be some resistance, I have offered to pay last, security, and an extra month for them to vacate.  

My first filter would be comparing the cap rate of the property [this is basically the operating margin of the asset] with your weighted average interest rate [ for example if you borrow $80k @ 3% and $20k @ 9% your effective interest rate is 5%] If your effective interest rate is higher than your Cap Rate, the investment doesn't make sense, at least in the short term.

Check with your mortgage broker to see what you may need to provide if you are on the deed... but I'm reasonably sure you will be asked to sign the security instrument (mortgage or deed of trust) since this appears to be a requirement in the Fannie Mae Selling Guide.

Conventional guidelines requires a lease, and no security deposit.FHA requires a lease, security deposit and proof of it being deposited. 

This implies that you basically are going to have a heavy weight (the insurance company) in your corner in any suit.One umbrella policy can protect all assets.  

But for your income property, they'll give greatest weight to the income method (the one based on NOI and cap rate as you said), as they should.You wrote "NOI divided by the Cap Rate" but keep in mind, the appraiser will use what they feel is a market cap rate, not the cap rate when you purchased the property or a cap rate you want them to use.

based on the information you provided, I would give it another shot and secure another tenant, and get a HELOC/cash out refinance to get another property.

Sometimes, a home warranty offers valuable coverage that you can use with no hassle; other times, it just provides a "sense of security" when a first time home buyer finally buys a house.  

This almost naturally ends up being a lower rate of return for security. 

The thicker concrete on the outside helps carry the weight, but really doesn't do much more.