I truthfully don't see a great deal of negotiation leverage as this building is the norm  rather than an outlier fact pattern.

I've had to do some work to the property (drain tile in basements, insurance claim for plumbing issue) but I knew that things like this would happen and I could stomach these expenses with my W-2 income. 

Based on your fact pattern (was a personal residence first and then a rental, not vice versa) I think you might be looking better.

.$70K purchase, only needs about $10K in paint, molding, tile...simple stuff.

Then the owner next to mine complained about wall damage and yet another owner complained and it turns out the guy above me tiled his shower floor and clearly didn't know what he was doing - water was damaging walls and ceilings. 

This involved new windows, tile, refinishing cabinets, adding a bathroom, updating a front porch, and several other things to bring this property back to life.

Can I tell you how many times in my last flip where I got the wrong faucet, paint, mortar, tile, (the list goes on...)

It's easiest to have the tile company do this at your initial closing, but you can do it yourself.

The fact pattern is missing WHY they would not insure.

The problem is it sucks, it barely works, it's surprisingly unintuitive for something so simple, and barely any guests actually use it.Which is kind of the same reason we're not discussing this on Google+ while wearing our Google glasses and talking about which version of Google Stadia is best to put into our homes as we communicate with our cleaners through Google Hangouts.While google obviously has a few big hits like Maps/Flights/Gmail, the majority of google releases follow the same pattern of great technology, horrible interface, no marketing, and eventual abandonment by Google.