There is a control module under each seat. I swapped my seats out and did the wiring for the heated seats and side adjustment a couple of weeks ago and noticed that each seat's control module has a different part number. They looked the same so perhaps you would be able to swap them around but it unfortunately it will probably require you to unbolt the seats to get to the underside.
I can't remember which of my seats this is from and I apologise that it isn't the best picture but you can see it's quite near the yellow connector:
I think you'd be fine with the airbag/tensioners though as they are just a direct electrical connection whereas the heated seat modules are controlled by linbus so obviously each module must be able to identify which seat it's for.
As for your pump issue it could well be that the pump is broken. There are only two pins required for it, pin 1 for the +12v and pin 16 for ground. If yours is attempting to make a noise then perhaps it is broken. It's easy to get to the pump though - can't remember if they're the same part for each seat, so you could try swapping the two around?