Are you willing to shadow him or her and do some errands on their behalf in exchange for the learning?

What they're offering you is called Lender Paid Mortgage Insurance or LPMI, in which they pay the PMI for you in exchange for a higher interest rate.  

Also, any property investor would just 1031 exchange the property.

The depreciation does not necessarily have to be re-captures.  1031 Exchange allows deferral indefinitely...However, if you are going to include depreciation, then include CapEx into the expenses :)

I have called several lenders in PR and they have told me they are not so welcoming to foreign investors.

The Act allowed the exchange of silver certificates for silver bullion until June 24, 1968.

App/Mobile tech bubble, Web 2.0 bubble, finance, international trade, foreign money, etc.

I've thought about the following:Sell all 7, take the ~250k after expenses and do a 1031 exchange to use as a down payment on a 20+ unit apartment complex (~1M or so)- this option would bring my career decision making process quicker. 

Living on a small little island in Curacao, coming to the USA, as an international student, finagling my way up the most desired organisations on this planet, in my field.. which is hard to do as an American, even harder as a foreigner.  

Another factor to consider would be the advantages and disadvantages of foreign income (Bahamas) versus income generated in a U.S. territory (Puerto Rico) - a good question for your accountant!