I have 20 years of training and hands on experience in the very skills you are referring to. 

To fix and flip, buy and hold, fix and occupy.What are you capabilities, how much cash on hand, what can you qualify etc.If you are just starting out a great way is to buy an owner occupied property that needs rehab, fix it up, occupy and refi, wait a year or two and repeat process.

It still rests in your hands to continuously check up on the status of the home warranty company.

So I do have 1st hand proof that they do indeed close some loans.

assessed value is always significantly lower than market value..also with prop 13 maybe its on sales price.. but same thing.. out here its not like other states were its just a % of what yo paid for it or what the assessor assess fair market value basically annually .. like you see what happens in Texas when things change hands. 

But, after about 10 months I started to get a little stir crazy and needed to get my hands dirty so I started surfing HUD and Fannie Mae sites for a fixer-upper.

What should be included in the hand-written message to garner the best possible rate of response?

Hand that over in person latest when you meet them after closing.

If its really something youd like to consider, then take the matter into your own hands. 

I have to agree with @Eduardo Sanabria, a property over $300,000 takes much longer and it's harder to sell in the area.On the other hand, great deals of rent and hold properties are much common in the area due to the massive renter's market, El Paso is full of renters due to Ft Bliss and the universities in the area.Good luck in your next flip!