If the answer is yes, then it's a no brainer to make minimum payments on your 2.8% interest rate mortgage, and use the funds that you would have paid extra to pay it down faster, to either invest in more real estate, the market, or anywhere else where you can get a ROI > 2.8%.If the answer is no, then feel free to aggressively pay it down as fast as possible, to become debt-free faster, and just have a large amount of money in savings or to splurge with.The bottom line is that your 2.8% mortgage is GOOD debt.

For your $2M property, a cost segregation study estimates $316K in first-year depreciation (compared to $28K with standard straight-line), potentially saving ~$117K in taxes at a 37% rate.

As U.S. citizens residing in Europe, we are required by the local tax code to hold the property in our personal name.

This can save thousands annually.  

About how they saved $6,000/yr for the last 10-20 years.

Real estate agents, property managers, and contractors who specialize in your target market can save you time and money in the long run.

You mentioned gross rents of $3400 per month and Principle/Interest/Tax/Insurance of $2500 per month. 

Avoid basing it on uncontrollable factors like taxes or insurance.

How is it for preparing taxes? 

Some people are able to save money and budget and others are not really good at it.