I am offering $260k.

Typically, they can give you the lowest rates However, another option that may be more beneficial is getting a LOC (line of credit) secured by the paid-off house.

The price could be affected by MTR vs.

I am hoping to make a low offer closer to 1 mil due to the time it has been sitting on the market and not paying a buying agent 3% but just using an attorney.

You also have options like 30 Year Fixed, 30 Year 5/6ARM, 40 Year and Interest only (maximizes cash flow).You are essentially acting as your own bank by using the equity and selecting the best rate/term to benefit cash flow.

Hemlane offers property management through our innovative model where we send 100% of the rent to you so that you can control and approve expenditures as well as have full transparency into the day-to-day so you always know what's going on and can make key decisions. 

I’ll either offer them a lease extension until spring or charge a MTM rate that covers 2 months vacancy.

If the deal makes sense, you could even offer slightly more on the backend because you'd be paying them directly for the downpayment Example: If you're looking at a $250,000 SFR, and the Downpayment is $12,500 (5%, for the sake of simplicity), you could ask the seller if they're willing to agree to Seller Financing if you raise it by $2,500 (to $15,000). 

An acquaintance of mine who does property management recently told me that there's some hack for paying off your mortgage sooner by paying the monthly fee in 3 chunks within each month.

Loans that are backed by real estate.