Thanks all for your wonderful comments - truly am humbled and honored to participate in this community.
I also took a chance to take a less photogenic picture of the side profiles of each - to show the thinness of the cases. Below the order from thinnest to thickest is 5140, 5712, 5575, 5164, and 5960. Just amazing how Patek can provide diversity of dials, but also of cases - which I imagine has more to do with the 240 vs 324 movement.
In any case, my initial thoughts for next piece is a) 5170P and b) 3970P. Like keks mentioned I could balance out with a Platinum piece and of course a different model - so both of these fit the bill.
Any feedback would be greatly appreciated - certainly the hunt will come hopefully soon!
Cheers
Peter