Thanks for the replies.
I have a copy of the owners manual, but it's very basic. You have to disassemble A LOT to get at this cover, so it's probably not something they consider user-serviceable.
I think you're right, it is shimmed, what I described as 'cups'. Point taken about grinding the stem, I'll see if a local motor factors or lawnmower spares shop carries any, if not then there seem to be plenty around online (once you know what you're looking for!).
The valve is not bent, has not struck the head, there is a uniform buildup of carbon around the rim of the seat and a great deal in the head itself. It's a very old generator so I think maybe the gap has simply worn down through use.
Cheers.