So they often will reduce the leverage of the loan (getting 65% instead of 75%) or deny it (which isn't as likely). 

You can get a normal owner occupied home loan to do this. 

The only way to pay down a loan, is to pay down a loan.

And if it were set up where everything went through a title company so the buyer pays the title company, they manage the buyer's loan (from me), and the title company ensures my mortgage is paid without my direct involvement... what parts of the transaction would feel risky or not worth the headache to you? 

Or, depending on the property you could go non-QM with like a DSCR loan and close in an LLC or partnership.

In response to your original question, closing agents should handle private loans just like a bank loan. 

In many countries foreign investors buying rentals can't get loans or loans at all. 

From my experience, you can use that savings to house hack with an FHA loan, invest in a turnkey property in a more affordable market, or even partner with others to expand your purchasing power.

Our area has a good selection of hard money lenders, and every now and then, you might find an owner willing to carry the loan, often at attractive rates.

If that's what you're really after I would start with the basics of what kind of bank loans either residential or commercial are available to you - not saying this is the best option, but it's a good place to start.