Just to provide an update on this —
I got the lathe sorted out. The problem was a combination of several — grease and filth packed deep into the tailstock and carriage, and unevenly worn ways.
Figuring I had nothing to lose, I removed the right side support and leadscrew bushing. Strangely this part feels like machined plastic, there's almost no weight to it.
The carriage needs to have the locking and forcing screws partly removed before it'll move – so the outer two screws (locking) need to be a few millimetres proud of the carriage casting, while the forcing screw in the centre needs to be removed entirely. At that point the tailstock should slide right off. Use the power feed or refit the handle temporarily to drive the leadscrew and remove the carriage.
At this point I gave the whole lot a good clean with WD40. I put a straightedge on the bed and slipped the feeler gauge in… revealing a depression a few inches from the left side. Not deep, just enough to screw up the locking mechanism in the carriage.
I refitted the right bracket to support it, then ran a 400grit oilstone down the ways to take the burrs off and level it out. After about half an hour of work I noticed the wear-marks in the worn section were starting to give way to the more linear pattern of the oilstone, gave it a few more strokes and called it good enough. Washed the ways down with WD40, gave them a good wipe and relubricated everything with 3-in-1 Oil before refitting the carriage and tailstock. "Reassembly is the reverse of disassembly" as they say.
There's still a slight rock over the worn section, but it's infinitely better than it was.
Now onto the next problem, the previous owner drove one of the support pins for the front carriage support into a blind hole! I'm hoping it's made of mild steel or similar and a magnet might persuade it out, otherwise I'll be turning a drill bushing and drilling the bugger out!
Sadly drilling a 1.5mm hole at the end of the blind hole hasn't helped… my assortment of pointy tools just can't apply enough force to push the pin out.
Oh, and then I have to fit the tumbler reverse… and fix the broken snap ring on the dog clutch…
Cheers,
Phil.
Edited By Phil Pemberton on 28/01/2019 02:14:04