These payment options can get up there!

Even if it does, there's closing costs to consider.As I said, I have no cash myself, so I'm asking how I can deal with generating cash for closing costs (and a down payment) if it comes to it.The house costs $139000.

I offer an online payment portal to submit rent payments via ACH or CC - they "couldn't figure out how to use it" so I set us up to accept Zelle payments.

This is the equivalent of a car salesman pitching the "monthly payment" of a car instead of the actual price of the car.

What would standard down the payment be? 

In this case, your monthly payment with 20% down will have a good MARKET rate if your DTI works with a much lower month payment and no mortgage insurance(MI).

I have a large lump sum saved in an investment account for down-payment and any additional costs.

Use the 20K as a down payment on the next house hack and don't touch your current properties equity.

Perhaps we "buy" the house from them for the $328K balance to satisfy the lender and don't need a large down payment and then have a separate contract with them to pay $x per month until we've paid the full $172K amount.

You will need to put some kind of down payment upfront.