Mentioned in the past, i used to make tooling and parts for a guy who built a few tables/year on the side for sale.
Also my regrets that i did not pay much close attention: "If there's ever a need for that, John will be around"
Anyway, one of the times he was trying to show me something & i was only half listening.....
He used titebond, and i believe he was showing me he generally just stacked the pile of slates up on a flat (Flat, really.) bench, on top of each other, to hold the wood flat until the glue dried. OTOH, I had seen slates in his shop with clamps over the wood, not sure if that was repair or new work. Probably he did it either way, depending. He was meticulous about his machining of the parts. Making wood flat and straight on the jointer, before running it through the planer. It's one of the areas we bonded (no pun intended). (Correct machining of wood)
Obviously i don't know enough to comment further, but having used multiple 5-gals of contact cement for formica & such, cc would not be my first choice. It's not always as flat or uniform thickness as a typical wood glue, nor self leveling.