I went back and looked at that multi-air actuator you linked earlier. It looks like the car uses a singular cam but then pneumatic <?!> actuators for the other set of valves? I'm not sure I understand, but regardless the diagram is an exploded view of the cylinder head. Basically it means they had to disassemble the top half of the motor to replace that part, which might mean they had it sufficiently apart to have missed getting a wiring connector re-connected. However, given your description of it still running hot AND rough, it makes me think they probably still didn't fix whatever was actually wrong.
That repair looked mightily expensive to be so useless. Man, as soon as that thing is looking like you might own it out of warranty, I might suggest pawning it off on some other poor unsuspecting shmuck.