I took some quick measurements. From I can find from google 53mm at the 21st fret is a touch on the thin side. So I'm guessing the PBG neck would be closer to 56mm at the heel as that seems to be fairly standard. I think I might take a bit of a gamble and next pay order a neck.

The thin neck
nut: 42mm
12: 51mm
21: 53mm
1/2 scale length: 314mm

LP studio neck
nut: 43mm
12: 53mm
21: 56mm
1/2 scale length: 312mm