Alan Ratcliffe wrote
As a matter of interest, did you try simply adding an extra thick washer or two to the rod? Sorry - should have mentioned that first. It often gives you enough extra tweakage as long as there is enough thread for the nut to grab.
That was the first of the two methods Andrew suggested. Second was the Truss Rod Rescue Kit. Happily they can do either for me.
I do find it strange that Andy's didn't seem to know about those methods of repair. I'm glad I asked around, otherwise I might have already spent money on a new neck based on their advice. I'll admit to not being an expert on guitar repair - amps and pedals are more my thing. I'm glad there are guys on here with the knowledge. Thanks for sharing it. 8)