Take advantage of that.I'm not telling you to go after "bad" areas because they look good on paper, but it is the paper that should be dictating your target markets.  

Does the lease dictate the right of the tenant to allow someone to stay until the end of the month?

The quality of your deal and the temperature of the marketplace will dictate the size of your fee.If you are double-closing, your buyer will pay a higher price than you are paying your seller.

I see situations like this as a way for you to build yourself positive equity and future security while paying less than the market around you dictates.

Your goals and circumstances will dictate. 

If you feel and the market dictates an offer of that level then do it (change agents).

Since it is dictated by case law I don't think a book would be up to date or practical.

If you allow the tenant to dictate terms and she talks to other tenants, it may not take long until they all revolt against rent increases and insurance requirements.

In the future, you should dictate what color the walls are painted. 

Lean what trigger are (one of my favorite's is Joe Sugarman's book by same name).Don't let your letter house dictate the lists.