., only your creativity limits how you resolve the issue.  

If the ownership situation has been or could be resolved (through probate, or possible other means), and the heir is indeed the sole owner, get an option to purchase subject to the taxes and liens and then use the pending sale as leverage to negotiate with lienholders.  

Does the deposit and last months rent that they paid to the landlord when they first moved into the property have to be resolved in any way?

That said, at some point trying to resolve this out of state will take more time / money then it's worth.

Possession won't resolve a defect in title or any claim adverse to your position as buyer, of course.QCD is best thought of to use to release an interest that is or may be present.

I have been in contact with their customer support and the problem still isn't resolved a week later. 

Find people there who are "compatible" with your goals.

As winter approaches, you need to resolve the issue, but you also need to hold the original contractor liable.

Hope this gets resolved quickly and painlessly. 

If it were me, I'd use seller financing with terms in note that push the rusk back onto the seller so that he or his estate do not receive the benefits of the equity in the note until the problems are resolved.