In other words, what time-consuming activities have to happen before closing, when the owner providing the financing is already pleased of the property’s value and condition, so there is no need for additional inspection, appraisal, etc.?

I assume the key issues are paying off the owner’s mortgage, recording the owner-financed mortgage, and being paid the title transferred to the new owner. But do those get done before or after closing?
The owner’s liquid assets plus the seller’s down payment will add up to enough to pay off ther owner’s mortgage.