Good morning BP - I have searched for a comprehensive answer to this without success.

Additionally, carrying a coverage of only the mortgage amount reduced my annual premium by quite a bit.

Any recommendations for carriers you've used during a BRRRR rehab and have been happy with their coverage/cost value?

Is the only other option to do an umbrella coverage?

I can get insurance elsewhere, but it is more expensive, and they exclude the dog from coverage. 

Generally, the first $1,000,000 of umbrella coverage is the most expensive.  

Brent, before you get into multiple LLCs you want to make sure you have adequate amount of liability coverage (part of the landlord policy).

@Joseph StamperIt’s worthwhile to talk to your CPA to develop a comprehensive tax strategy.

I’d recommend making a more realistic offer to begin with, including all the stops: appraisal gap coverage, escalating clause (if they’re being accepted), heart strings letter (not being looked at much in my market because sellers are getting so many offers, but doesn’t hurt), waive whatever contingencies you can/feel comfortable with, use cash or if you don’t have cash use a “same as cash” program that allows you to make a cash offer then finance immediately after closing, make the inspection “for informational/health and safety purposes only”, etc.

Let the insurer's claims counsel figure out the remedy.I don't see that lenders coverage was issued and regardless, it sounds like the tax sale purchaser/lender created or assumed the problem.To me it sounds like this may involve a defect in the original tax sale foreclosure... such as a lack of notice to all interested parties.