I think I see what Paul did to secure the pickup to the guitar. He might have formed a loop out of the securing arm and used a screw placed through the loop to secure the pickup to the bridge at the unused hole. He had to do something equally innovative to secure the pickup on the treble side. Unfortunately his hand blocks the view...
As far as I have found, testing with my own guitar+pickup+cable (=I haven't still tested it with the pickguard off. I should do it!!), the pickup is secured by means of:
a) The upper bridge's screw, that 'holds' in place the jack socket...
b) The 'black plastic strip' from the original pickup/pickguard assembly (=white in my guitar, black in his guitar) UNDER the pickup (=over the body of the guitar). This 'plastic strip' acts as a wedge. So, the pickup is 'firmly' secured between the upper bridge's screw and the 'black plastic strip' (=and placed off-center, as you said, to 'capture' only three -or four- strings...)
With this position, the lower pickup 'arm' falls EXACTLY at the outer side of the trapeze (=it's not seen at his photo, but it's seen at mine). So, probably a loop is hidden under McCartney's hand, tying the lower pickup 'arm' and the lower trapeze 'arm'.
But, again, THE THING is still puzzling me...
...The pickup arms were designed for securing the pickup to a fretboard. Paul chose to mount the pickup at the bridge for a sharper tone...
That could be the reason. But in a system like that, the jack socket has to be facing the sky, not facing the earth. Otherwise the cable would fall down over and over, would disturb when playing, etc. As he is left-handed, the only choice to place the pickup with the jack socket facing the sky, is by the bridge...
Hello Goodbye: thanks again A LOT for your help!!
Xosé