Whether you attach a hot lead to the pot center or (the correct) side will make no difference - all the way left will still be 0 Ohms and all the way right will be 500K Ohms (when wearing the bass). That's all a pot does, the resistance between the outer 2 tabs is constant; the pot's max value (assuming 500K) and the middle is the wiper that moves with the knob action along the resistive track, so as long as the same outer tab and center are used, the result (resistance between those 2 tabs) is the same no matter if center hot or not.
So all you need to do is take the pup and switch harness, as is, out of the bird, and when you drop it in the SX, connect the wire labelled "Output 1" aka hot to the center (vs side on the Bird) tab on the appropriate volume pot, with "Output 2" aka ground, going to the pot casing as before.
Note: this assumes that the way the Bird and SX were originally (currently) wired up has the pups in phase. If, after you do this, it sounds a bit off when you run both pups on the SX, try swapping the hot and ground leads at one of the volume pots (doesn't matter which).