You cannot appeal to have it removed or have a new appraisal completed.  

One thing that we had was a bug book or record book of each unit that was treated and what the bug guy found.I would take this to court with me if I had a eviction action so I could prove if the tenant ever brought this up as reason for non-payment, and had proof if we treated and when. 

If the previous address is close, march into the court house and look up the criminal and civil filings under the applicant's name.

Spruce it up, fix the curb appeal and market the desirability.

Having 2 structures (with the SFH on its own property/yard) is an appealing aspect of this deal.

If they fail to comply then your next course of action is to file eviction action for "Cause - Failure to vacate after lease termination/non renewal notice, look up your county court house and get the paperwork for that ahead of time so your all set.Don't bargain, BP forms category may have forms you can download for notices.. 

Is there a general area that's hotter in terms of appeal to military tenants?

It can also become an issue if you are preparing for eviction and the tenant deposits $10 just before court then comes in with the receipt.  

Off the top of my head.fire damagedvacantprobate /estatesout of state ownersburnt out landlords (think rent court)

However, this required my team to go to the court house several times a month to receive only a handful of leads.