What kind of documentation for used engine would satisfy you?

Depends what you're asking for it $$ wise. I've bought engines without hearing them run for a few hundred and had no problems, maybe I've been lucky but I generally look at the appearance of the engine, the seller, and the seller's property. I have also bought dozens of salvage vehicles from insurance auctions and only once got a car with a bad motor.
I guess if I was paying a couple thousand, I'd want some proof that it is what the seller claims, either video or hearing it run before purchase.