All fixed.
It looks like the problem was a combination of factors.
The handle and bushing came off easily enough with the screw held in the 4" vice with soft jaws.
The tailstock feedscrew was a bit banana shaped so we straightened that out.
The tailstock quill measured up parallel and round and was free of burrs etc so no dramas there.
The "bushing" that locates the feedscrew in the body was burred up so we cleaned that up in the lathe. But it was not clear if the grub screw that locates in a groove around the periphery of the bushing was supposed to hold the bushing firm and let the feedscrew rotate in the hole in the middle of it, or if the grub screw was supposed to sit in the groove but let the bushing rotate in the housing on the OD.
So an executive decision was made and a small divot drilled in the groove in the bushing OD with a largish centre drill, and a longer grub screw with a lock nut screwed in hard so the bushing stays put. Where it had been rotating before had allowed the grub screw to chew up the groove.
So then we had to install the handwheel, screwing it on until firm then backing it of an eighth of a turn and holding everything in position while nipping up the locking acorn nut.
Reassembled everything with plenty of Never-Seez and all is good.
It looks like a pretty cheap and nasty design with the bushing grub screw that sort of locates the feedscrew bushing and sort of holds it firm but sort of lets it rotate too. When you crank the handwheel such as when drilling large holes etc, all the feeding force is taken by that grubscrew locating the bushing. It is only about a 3mm grub screw so will not take much to shear it off. At least now it is positively located so should endure a bit better.