So... once the paying work was done for the day, back out to the shop to clean up the chuck. Using alcohol, a rag, and a screwdriver to help get into the corners, I removed all the obvious dirt and grit. Once it passed the "thumb test" (fingers/thumbs are great for feeling out grittiness), I got on with stoning the corners of the scroll. There were a few lumps, bumps and sharp edges. Half an hour later, and it was nice and smooth feeling all the way around both edges. I've no idea if the faces are any good... just have to hope there. Again, liberal quantities of 99.9% IPA (Greene King's finest) was applied to a rag & shoved around the scroll using a screwdriver. Once "clean enough", re-assembly could commence.
First.... a note on fit & finish. For the most part, it seems excellent. The scroll is a really snug fit on the bore, the backplate (just cheap aluminium) is near enough. But weirdly... one of the pinions is an odd-man out. See if you can spot why in photo 11....

Not too big a problem, fortunately, there's still enough meat on the end that it rides OK in its supporting hole. If it ever causes an issue in the future, I reckon I can fix it with a bit of welding & turning.
So - photo 12: Apply enough grease to get a high-speed weasel up a drain pipe... I also greased the pins that locate the pinions. At this point, the chuck turns easily and smoothly with just one finger on the chuck key... Re-attach the back plate, and flip over. Weirdly, that made it a little harder to turn, I'm not sure why exactly
Moving onto the jaws, I noticed that 5 of the 6 had a nasty little burr on one corner of the "T-slot". Jaw #1 didn't - I wonder if that's the "quality control" jaw, and whoever was on deburring duty that day was feeling a little, shall we say, work shy...?

Anyway, my concern was that they'd be trying to scrape away at one of the running faces, and being right on a corner & fairly prominent, I wasn't sure how long they'd take to stone out (or even if I'd damage my stone)... so on the off-chance, I had at it with a file. To my surprise, it worked.... so obviously the jaws aren't as hard as they could be... There was also a sharp edge on the bottom of each jaw, the part that sticks out in front of the scroll. I filed those a bit too; they wouldn't be an issue in use, but it's one less place to cut a finger.
Photo 13: All back together again. It's still stiff to turn, but nothing like as much as it was out of the box. It feels a bit smoother too (not that it felt bad out of the box). I did notice, per one of the YouTube videos, that if you clamp it up just using one pinion, then one of the jaws doesn't quite tighten - you have to go around and tweak up each pinion in turn to get it fully tight. This is not a problem, I already have to do that on my 3-jaw to get anywhere close to concentric with it, so I'm already in the habit of tweaking each 'ole.
All in all - so far, I'm a happy (Easter) bunny. So for my next trick.... I'll turn up a "go-nogo" gauge plug for the Edgwick spindle nose (more like a "go" gauge, I can't be bothered having a "no go" as well..), I can then use that when cutting the lathe-facing side of the backplate, rather than having to constantly take it off the lathe & back on again to test fit. Watch this space (but don't hold your breath.... first baby is just a couple of weeks away, if he's on time, which will put a serious dent into workshop time). I need to get back to restoring that Boxford, so I've got
something to play with while I'm stuck at home!