I would suggest you do a lot of home work on the company that wants to rent your home for this.

I do like your math. 

Houston's diverse, and the real estate market is buzzing.Check your budget, how much risk you can handle, and what you want from the investment.Montrose, The Heights, Eado, and Museum District are buzzin' with mid-term rental potential.Research the neighborhoods, check the rates, and do the math on costs before diving in.

There is so much math involved and I have myself doubting all the scenarios to see which is clearly the best way.

@Victoria Spagnolo  My quick math shows it would have to appraise around $260k to refinance it and pay off the $50k

Which doesn't mean STR's aren't possible here - it means you have to do your homework! 

There are good and bad with everything, but for people who can't pay <$100 a month for part of their rent, you really have to wonder what they do.My mathing might be wrong but for the 93 her full rent is 1400.

The math is:168,800 - (337,500 - 12,000 - 255,083.96) = 98,383.96

It’s rarely the ARV math that kills an investor.It’s not usually the contractor bid (though those hurt).It’s not even paying a little too much. 

I just can't see the math working.