You can often find unique items that catch the eye. 

I focus on mid-grade quality items that are durable and pleasant to use yet not so nice that people are tempted to swipe them and are then expensive to replace.

After some research online, I am reading that the cost per square foot on a gut renovation of this nature in Stamford CT is anywhere from $150-$350, which is ultimately not very helpful, because at $150 per sq ft, this is a very appealing project with a total profit of ~$175K (46% ROI) and at $350 per sq ft, it very much isn't, because it would be a net loss of 83K (haha).QUESTIONS:What can I do refine my estimate a bit given that I am not allowed to a formal inspection on the property? 

For Non-Admitted carriers, the important item to then pay attention to is the AM Best rating (or equivalent rating agency).

You'll just add to your losses and still have the same mess to clean up.The process for abandoned property is to give written notice to the tenant at their last known address (your rental).

If you continue using it as a rental but reduce STR activity below the material participation threshold, your deductions may become passive and subject to loss limitations.2.

Throughout the year I come across situations where people need to sell there home due to a variety or reasons, job loss, income loss, health, divorce, etc.

For items not available before the SoE and hitting the market after the SoE, you can raise prices a max of 50%.

Also what towns do you primarily rent in and how much of a loss do you take vs renting market rent?

I personally would sell it.Your return from real estate is two items - Cash Flow + Appreciation.What is the annual rate of appreciation you are getting, approximately?