Offset Gains with Capital Losses: If you have other investments that are currently at a loss, selling them can offset the gains from your property sale, reducing your taxable income.5.

I figure my options are to sell and take a loss (not ideal), or preferably find coverage that allows or doesn't care about the K&T.

That, combined with hidden repairs combined with self-managing a low income could all construe to thousands in losses. 

Quote from @Landon Mizuguchi: @Michael Plaks if you're living in the house and renting rooms  (e.g. room hacking) you can't claim losses?  

Defaults and Remedies A default exists under this note if (1) Borrower defaults in the payment of this note or in the performance of any obligation in any instrument securing or collateral to this note; (2) (a) Borrower or (b) any other person liable on any part of this note (an "Other Obligated Party") fails to timely pay or perform any obligation or covenant in any written agreement between Lender and Borrower or any Other Obligated Party other than as described in (1) above; (3) any representation in this note or in any other written agreement between Lender and Borrower or any Other Obligated Party is materially false when made; (4) a receiver is appointed for Borrower or an Other Obligated Party or any property on which a lien or security interest is created as security (the "Collateral Security") for any part of this note; (5) any Collateral Security is assigned for the benefit of creditors; (6) a bankruptcy or insolvency proceeding is commenced by Borrower, a partnership of which Borrower is a general partner, or an Other Obligated Party; (7) (a) a bankruptcy or insolvency proceeding is commenced against Borrower, a partnership of which Borrower is a general partner, or an Other Obligated Party and (b) the proceeding continues without dismissal for sixty days, the party against whom the proceeding is commenced admits the material allegations of the petition against it, or an order for relief is entered; (8) Borrower, a partnership of which Borrower is a general partner, or an Other Obligated Party is terminated, begins to wind up its affairs, or is authorized to terminate or wind up its affairs by its governing body or persons, or any event occurs or condition exists that permits the termination or winding up of the affairs of Borrower, a partnership of which Borrower is a general partner, or an Other Obligated Party; or (9) any Collateral Security is impaired by loss, theft, damage, levy and execution, issuance of an official writ or order of seizure, or destruction, unless it is promptly replaced with collateral security of like kind and quality or restored to its former condition.

So for him, paper losses are good.

Or the market tanks and the value of the house goes down and that creates issues (selling at a loss, who brings money to the closing table, etc.

Would you prefer they change their policies just to fill your rental quicker and then increase your risk of losses?

Some carriers offer loss assessment insurance, which can come into play when the HOA experiences a large covered insurance loss, such as a hail storm requiring roof replacement or a fire requiring building replacement.  

You'll want to keep track of these because they can Increase or decrease your at-risk amount and as a result the losses you can take as a partnerYou or your CPA will need to report these on your IRS Schedule K-1s for each of the partners in LLC. ...