We've got expenses dancing around $2-3k per month, a modest $10k stash, and a student loan payment ($725/month) the size of a small country's GDP.

As long as you don't increase your total current expenses to obtain another property.

The MTR rent is currently lower than the LRR rent even 1 year after the quota went into place.  

For a refi, there are lenders that will go a bit lower.

However, I think, with REPS, we can deduct the expenses and depreciation against his W-2/K1 income which make the overall picture look appealing.

These are complex and expensive. 

We really want to stay in this part of town, but buying a multi-family or single residence home is so expensive.

Older buildings likely have nothing but one layer of sheet rock between the floor boards/joists and lower level units.

I am ok with expensive if ti gives me quality.

The problem now is that the golden visa has been abolished, Lisbon has gone from cheap to very expensive and new short-term rentals have been banned, whereby investing in Lisbon has become much less attractive.