He casually told me he sends out 10,000 pieces of mail every month. . .ten thousand! 

It'll likely take a month or two assuming that the loan is with one of the large servicing companies that move at a glacial pace. 

Reliable, thorough housecleaning services can be challenging to find.

For example, if the loan officer asks you what your monthly payments are and your mother-in-law moved in with you because she is struggling financially and you are paying her car payment, don't share that you are paying her car payment every month.

However, when I'd want to buy a property in Mexico, I'd want to hear from real estate agents who would provide me the best possible service.

That they don't service their loans well, lag on draws, say they can close fast but don't etc etc.

PM is a service business and time is very valuable.

If I managed the properties myself, I would save about $900/month.

There's a value to that service.

One month of vacancy will cost you $2,600 + $200 utilities.