Not being a USian: what does turning the AC down mean? Set the thermostat to a lower temperature or make it less active (i.e. set it to a higher temperature)?

As someone who's been in a room with many people: I'm confident it means that the temperature should be low, because the room will quickly heat up otherwise.

(This is also the reason I'm hesitant about the oven tip, given that the kitchen is where the true party is.)

Right, it means to turn down the Air Conditioning to reduce the temperature of the hosting space first. The reason being that as people arrive, temps will climb into something more comfortable.