Right now my tenant has told me she is staying an extra month after I offered the extra time and she refused.

Many of them will succeed, many people will get burned.

My first out-of-state investment was turnkey in Tennessee and I got burned really bad...I bought at the bottom of the market too...couldn’t keep the property occupied for more than 3 months at a time and the A/C condenser kept getting stolen even with a locked cage!

Neither of us have broached the topic of renewing their lease term, so at this point I'm assuming they are planning to stay and would like some extra time, so I thought it might benefit us both to end the fixed lease on 6/30, and then start a new month-to-month lease with a 1 month term and 30 days notice, all on 7/1, with some language built in for their leniency on showing the place to prospective tenants.  

Property management companies are asking extra charge for initial setup2.

This extra amount is disqualifying me to obtain the loan.

But I’d give the required notice, maybe even an extra 30 days and raise it to market rent for the condition, probably another 75-100 a month. 

this seems like a high amount that they somehow burn through each month.

Better luck and better prospect with Marriott and Hilton brands, to get some good management companies - ultimately costing you 20% or more of the gross - when you add their extra-expenses of over staffing and unwanted maintenance and repairs bills, and, using their unused-resources to bill "your property" for services etc.

House 1 you say is move in read, so if you plan to offer $42K, where does the extra $5-10K invested come from to get $47-52K?