Ok here goes.

The humbucker is phased incorrectly to the middle pickup. You have two options to get round this.
1 reverse the green and black wires on the humbucker, as you've already been advised. (the simplest solution)

2 reverse the wires on the middle single coil, then the neck single coil, to keep the RWRP relationship between the neck and middle pickups. (100% more work than reversing the humbucker polarity).

Your choice mate.
The problem isn't the Humbucker or the Singlecoils. It is the circuit. The pickups don't work together properly in circuit. It's a common problem when mixing pickups of different origin.

Thats all there is to it.

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No no and no

Not on Texas Specials as in a Strat they are calibrated for their position of neck and middle pup and reverse wound/reverse pole will cease to be.
Plus if the OP installs a coil switch then he will need that set up when bridge is in single coil mode with the mid pick up....

I think the easiest is to remove the TS's and use them elsewhere with the Pearly Gates HB.
It's really a Blues/Rock set up not a grinding Raimmstein sound.

Then match the Neck and middle single coils to the Duncan distortion.
Having a combination of three pickups, HSS is always a compromise, which is why most setups for Metal are either three split rails (hb's) or 2 Hb's or just one HB in the bridge....
It all comes back to the output of that bridge pick up....
This is the problem today where everyone is searching for that perfect pickup set without taking into account the guitar and the amp you are playing which are the other 2/3rds of the equation..
My CS 56 NOS Strat sounds like crap if I use it to play any George Lynch, UFO or any of that genre. The pups are not up to the task, pure and simple...
Adding distortion just makes a bad sounding pickup worse...Bad in the sense that it is totally inappropriate for the app....
Texas Specials and 69 pups will get you that Knopfler tone but not Malmsteen's...

Sort of like having a Halogen headlight on the passenger side of the car and a Xenon HID on the driver's side. My B6 Avant would be throwing fault codes all day long.

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