Here’s how I’m currently thinking about it:The interest rate on my existing property is 3.5%, so I’d like to maintain that rate rather than refinancing the entire loan.

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

Again, the $600 interest threshold is per loan, not per person.But this was not my money!

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

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

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? 

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

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.

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.

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