it's possible to replace the thermal pad and put a thicker one.
It's more like 5 mm. So already thick.
I have no idea how far into 'tweaking' you tolerate but,,,
On previous boards if you overtighten the heatsink it causes the board to bow (curve)
You might put a screw driver on the holddown screws and try adjusting while observing the VRM gap.
One must assume that KnC uses unskilled drunken illeagal aliens for assembly labor and plan accordingly.
If the plate is thick enough to hold a bend, it might be bent to match the curve of the board.
Optimally use seperate hold down for main heatsink and contact VRM heatsink directly on VRM's.
(IE: buy standard heatsink holddown for Intel LGA115x)
(Assumes the hole pattern is still 75mm)
Could also glue copper washers to top of VRM as spacers and remove or thin foam spacers.
(J.B. Weld is common thermally conductive high temp epoxy, else Artic Cool makes a thermal adhesive)
Foam is a shitty heat conductor.
Another easy tweak is to add M3 male x M3 female hex standoff to raise board for better bottom of board cooling.
A plug and pray nightmere, a HW tweakers eye twinkle
YMMV
P.S do not glue VRM directly to heatsink as FrankenHoopiter customers have posted pictures showing the covers are not mechanical stress tolerant except in the down direction.