In a seller's market it can be tough to negotiate contingencies for extended closings contingent on your 1031 but it is certainly worth asking. 

Be polite and see if he'll sign a contract to extend with the loss added to his future contract? 

If the Seller is unwilling to grant an extended due diligence period then the price should be lowered to reflect the risk your taking. 

Given that there isn't all that much attractive in my immediate area (cap rates are very low), I am more or less location agnostic for my next purchase, and would be willing to fly/drive extended distances if I found property that was attractive enough.Ideally, I'd like to be able to perform a top-down analysis, filtering out cities with very low cap rates, and then further filtering based on macro-economic data to find markets that I would consider attractive from both a cashflow and appreciation standpoint.

Not saying don't raise rent to market, especially if they are far below market, just recommending you balance your desire to get top rental rates with the risk of extended vacancy and lower quality tenants...and if you price above market in an area of ample supply that is what you will likely get.

We ended up have to extend the deadline of the sheriff sale for 1 day to be able to close on time.

Continue with the evection, extend or put it on hold till he leaves, then assuming he leaves as agreed you drop the eviction.Without the esstopal you do not have any legal grounds to fight.

If it works out and she stays, I'd keep her on month to month at a higher rent rather than extending to a longer term lease.  

That is astronomically low for the SFR management industry.We have extended, through lease renewal, 1,025 expiring leases this year and many at no charge to the owner.  

or see if the current owner's insurance company will extend to you