Not sure what this site's rules on necro-posting are, but I'm just under 6 months so I hope it's alright.
Anyway, I've finally diagnosed (part of) the fault - the fuse installed was a quick-blow type, presumably being tripped by the initial rush of current to charge the power supply capacitors. I've since installed a slow-blow type, and the unit (amazingly) switches on!
Now onto the deeper issues.
Once the scope cathode had been allowed to warm up for a while (~30 seconds), with an audible 50Hz hum (presumably from the transformer), I could see a single trace present on the screen. However, it looked very unusual - rather than a thin, green line, faint spots of green were visible. Trying to adjust the position of the trace has no measurable effect. The only controls that I could successfully manipulate were focus and intensity.
Worrying that leaving the system energised could cause further damage, I unplugged the unit at the wall.
Any advice on what measurements to take?