She paid rent till the end of lease. 

However, if the property is partially rented out, will 6 months of the full mortgage have to be saved for consideration or will 6 months of the difference between the mortgage and rental income suffice?

I am only asking her to move out for 6 nights but what she is demanding will cost me ~2/3 of the rent.

For tax purposes, you are better off if you do NOT exceed the larger ofa. 14 days of personal use per yearb. 10% of the days it is rented as an STR (example: if it's rented for 300 days, you have 30 days of personal use before you lose tax benefits) 

For example, minimum 650 credit score and 3x rent for gross income.

I have a LTR that I've been asked to rent for 6 months.

HI Jordan,You can always start off by house hacking meaning you live in one UNIT or ROOM and renting out the other vacant units/rooms to offset your monthly mortgage payment.There are several ways to run and make sure you are maximizing your rental income while keeping your living expense as low as possible.

We're considering renting it and paying that amount in rent downtown to equal the mortgage payment.

When you say you want to put it on the market, do you mean to sell the property or to rent it out? 

I offered not to raise a rent and if they extend, they could cancel any time to buy their house.