Job done!
Only took me a day and half of blood sweat & tears, but my new cylinder is installed and working happily. I don't think I'll be giving up the day job though.
I tried ChrisR's suggestion of mending the old cylinder with solder, but either it didn't stick well enough or there were other pin-holes I hadn't spotted. Next time I would definitely take up Softus's suggestion of LS-X - easier to apply and doesn't cause cylinder insulation to catch fire!
So, after the failed solder fix I replaced the whole cylinder, consoling myself with the thought that a mend would probably have only been good enough for a bank holiday emergency and not for the long term.
Most of the problems were due to the postion of the heating coil inlet/outlet being different on new cylinders, meaning I had to re-arrange the 28 mm pipework. Trying to un-solder old, damp, painted-over pipework is a pain. As is trying to re-solder new pipe to it.
Anyway, thanks for all the helpful advice. I'm well satified now, and saved a packet too. 'Course, you may see me come crawling back again if the darn thing springs a leak a few weeks down the line ...