If you're getting hum in humbucker mode of either of the 2 p-rail pups when they are active all by themselces (i.e. just Neck active or just Bridge active), then either there is some part of the wiring job that is not quite right, or your guitar needs shielding.
And unless you wired the stk-4 to be split in positions 2 and 4, then you won't get hum-canceling because there would be an uneven # of coils active (the 2 coils of the hum-bucking stk-4 middle pup plus the coil of the bridge or neck that its being paired with). Hum-canceling is only possible when the number of active coils is an even number.
Also regarding the STK-4, we'll need to know if you ordered a Middle Position version of that pickup or not. Middle Position versions of this pup are different (reverse wind, reverse polarity (RWRP)).
If you post some pics of the wiring work inside the cavity, then we can try to begin to troubleshoot.
Also, please post a pic of the wiring diagram that you used.