Roger, I was thinking about the string going from nut to bridge, which in your case would leave a gap that is significantly wider than 1 mm. And you're not even having problems fretting the strings?
 
I'll try and take some measurements when I get home.

Unfortunately I don't have the proper tools to take these measurements. As far as I could tell, the relief with the string pressed onto the 1st and 24th frets is significantly less than 1 mm (as in: I can't see how an end of a G string could fit between fret and string). In this experiment, the string does produce a tone when plucked, but there is some fret rattle - more on the treble side than on the bass side.
 
Regular string height at the 12th is roughly between 2 and 3 mm, with the G string raised the most. There is no fret rattle.
 
The bridge is definitely not sitting on the top surface: there's about a 2 mm gap between the top surface and the underside of the bridge on the treble side, and about 4 mm on the bass side.
 
In all, perhaps you need to tighten the truss rods a bit to reduce the relief, then you should be able to raise the bridge off the surface.
 
HIH

What I've now done, based on the advice all you kind folks have given me, is to tighten the truss rods to remove most of the relief.  The bridge is now still flat on the baseplate, but I really don't think that the strings could go any lower and the instrument still be playable. So I've got it to where I wanted it.
 
Thanks for everyone's help and input to this, much appreciated!
 
Cheers,
 
Rog

Whew!  Glad to hear you solved it without filing anything.
 
Peace,
Darrell

Like a lawsuit?

Roger's English like me. We don't 'do' lawsuits ;-)
 
graeme

Better get Roger's Thesaurus Rex inlay out then.

Graeme's quite correct - instead, we do 'sue the b*stard'!
 
Rog

Then who burnt the custard? Ah, it's Jamie Oliver! The Golden Essex Boy Wonder Of The Blow Torch!