Everything Axe Unexpected Buzz/Hum

[Fuzzy John]

I replaced my standard pups on my MIM Strat with an Everything Axe set expecting to get rid of the noise.
To my surprize the noise is still there. Not as loud as befor, but still there to annoy me.
I searched this forum for an answer but found nothing that is close to my situation.
This is what is happening: the buzz/hum disappears when I touch the strings. This indicates to me that the bridge ground is OK. It also seems to indicate a grounding issue. However, when I put the 5 way switch in positions 2, 3 and 4 there is no noise at all when I do not touch the strings. The only time I get the buzz/hum is when the switch selects the bridge or neck pup by itself. Sounds like the bridge and neck pups are single coil.
The 2 pups in question are wired as per the diagram (white and red together and taped, green and bare to ground, black to the switch). The resistance appears to be OK (double the single coil resistance).
The control cavity is factory shielded (looks like paint) and the grounding wire to ths shield appears to make good contact. The pickup guard has the foil covering most of its back and the ground contact there is also good. The output jack appears to be OK and the contacts are good.
At this point I am at a loss, so I would appreciate if someone could point me in a new direction.

[GuitarDoc]

You say the hum goes away when you touch the strings. This means that the bridge is NOT grounded. Don't forget to check the connection of the ground wire to the tremolo spring claw and to one of the pots.

[frankfalbo]

You say the hum goes away when you touch the strings. This means that the bridge is NOT grounded.

In my experience it's the exact opposite. Touching the strings = touching ground.

[Fuzzy John]

You say the hum goes away when you touch the strings. This means that the bridge is NOT grounded. Don't forget to check the connection of the ground wire to the tremolo spring claw and to one of the pots.

Well... the "old" meter shows 0 Ohms between the output jack shell and the strings.

[itsall4you]

They're single coil pickups. You're not going to be 100% noise free.
The reason why there's no noise in position 2 and 4 is because those are the 'in between' positions. The two pickups selected cancel the noise out.
Check if your position 3 actually makes the noise go away. If it does they're maybe another problem present.

[Fuzzy John]

They're single coil pickups. You're not going to be 100% noise free.
The reason why there's no noise in position 2 and 4 is because those are the 'in between' positions. The two pickups selected cancel the noise out.
Check if your position 3 actually makes the noise go away. If it does they're maybe another problem present.

I have the Everything Axe set. According to the product page all 3 pickups are humbuckers not single coil.

[speed2dirt]

In my experience it's the exact opposite. Touching the strings = touching ground.

So what would be the solution if this was the case?