Is it possible to swap the positions of the two units in your installation? The player may run a bit cooler on the bottom, depending on where your head unit is generating its heat.

Yeah, unless they're mounted so close together that the cooling fan doesn't have anywhere to exhaust the air. But if there's a bit of a gap between the two, then yeah, headunit on top is the way to go. That way the heat from the head unit doesn't rise into the player and cook it.