With the bridge set to its lowest position, the neck clamped in place and strung with proper E and G strings the action seemed very high so I set about making a shim...
First attempt was cut from a piece of mahogany on my bandsaw... I estimated that something around the 2mm mark at its thickest would be the place to start then sand it down to get the string action about right... the thinnest I managed to cut without breaking was about 4mm at the thick end so it time for a re-think (and I really didn't want to spend too much time on it as I wasn't really sure if it was necessary). So rather than try to reduce something to the correct size I decided to step laminate three pieces of cherry veneer I happened to have, alternating the grain like plywood. I sanded the stepped side smooth and ended up with a shim 1.75mm at the thick end tapering to a wafer-thin 0.25mm. I trimmed it to size leaving the thin end 2-3mm short of the joint line so that it won't be seen and also so that the shim effectively tapers to nothing.
With the neck and shim clamped in place, I adjusted the bridge so that the bridge could still be lowered a bit then measured the distances at the penultimate fret at the body end (I couldn’t get access to the last fret as my F clamps were in the way). I took measurements with open strings (the nut seems quite high at the moment) and also with a capo strapped accross the twelfth fret:
Without shim (open 12th)
E 7mm* 3mm**
G 7mm* 3mm**
With shim (open 12th)
E 1.5mm* 0.635mm (0.025")**
G 1.5mm* 0.635mm (0.025")**
* measured approximately with a ruler from the fretboard to the underside of the string
** measured with feeler gauges (plus the thickness of the rule when unfretted without shim)
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