Based on my experience with hoarders - Leave it alone.Unless they are causing damage you really don't want to spend your energy chasing that.

I'll be moving to McGuire AFB in New Jersey and am looking for my first property within an hour of the base.

They lowered the price a couple times and then I offered another 6.9% below that and we have a deal.I suspect they have a mortgage at 3.6% based on when they last got financing and I REALLY would love that rate, so much that I'm open to re-doing the deal much closer to their most recent listing price if I can get the house subject-to the existing mortgage and give them cash for the difference. 

Everyone does it a bit differently based upon their experience.

Here are some recommendations based on the limited information you posted:Yes, I would get the chimney flue installed.

Based on walkthroughs of the property, they may offer estimates that are more accurate.

Regardless, I’d still like to get a month contract with these stipulations to make sure the bases are covered.

Generally options will vary dramatically based on these unit buckets2-4 5-1011+

LegalZoom is $299 and RocketLawyer is free (already subscribed).Based on the set-up questions LegalZoom seems more succinct/precise for a trust with a single asset.

Two AF bases there, which is usually a good sign for the rental market.