An idea that occurred to me is the possibility of putting these 13 rentals into one bigloan and doing a cash out refi to cover a large part of the cost of our build, with the thought that the interest would then be deductible, which might have some tax benefits. 

I am looking for the most economical way to leverage a free and clear duplex I own (worth appr 120k) to cover the down payment (appr 35k).

So if you buy at 70% or ARV minus repairs, the financedd amount will be enough to cover repairs and an additional 5% additional.

The other challenge, in my experience, is that a lot of the properties are ~80-100 years old and are suffering from deferred maintenance.

From my moron contractor that lied to us he was licensed in plumbing and electrical.. that did all the wiring and plumbing and then covering it all up with sheetrock, trying to scam the city into thinking no one touched electrical, to not ever having a single inspection done, then stealing money from me, and running, and buying the cheapest material.. ever!...

(For this scenario, please assume closing cost will be covered).

The only utility the landlord must cover is water and sewer.

They usually rent them out the entire ski season to the same renters from Manhattan and they tell me that the income covers their year round mortgage and maintenance costs.

However, your landlord is likely notifying you of  the complaint because there are sufficient complaints from her other tenants to warrant letting you know; concerned that other good, quiet tenants may leave if the issue is not resolved; and covering herself in case there is an actual drug issue. 

I recently learned that the safest seconds are those where the first is performing, and there is enough equity to cover both the first and second position.