Ok guys, I made some progress: I took a day and I drafted up the schematic of this board, at least partially. I excluded the high voltage side. Couldn't work out precisely what Q2 and Q3 are. I'm not even sure they're NPN to begin with - they're marked as SS1 or perhaps SSI and I've drawn a bit of a blank on trying to figure out what they are, so I did the next best thing and just speculated based on how they're connected. Aside from the values of the caps which I didn't bother to remove to check, everything else should be correctly marked and measured.
Also, after a bit of digging around my colleague's desk, I managed to find the original current sense resistor. Big surprise: he must've got the color code a mixed up when he got these big ceramic ones, because the original is a 1.5ohm resistor, whereas the one I found on the board is a 0.15ohm one. He probably messed up at the last ring. Anyway, the original was indeed open, so I just replaced it and sure enough: now the board comes on as expected, with just a single flash of the bulb. I even took it one step further and plugged it in directly and it's stable....well sort-of: it doesn't regulate properly. The output voltage is too low, at an unsatisfactory 9.7v. I imagine it would be even worse with all 3 relays trying to pull in at once - might not even start at all then. I replaced UC3843 again and the same thing happens.
I took a look at the board with a thermal camera and the IC does get a bit warm at around 37c, at least that's what the camera tells me, both on mains and powered directly with 12v. R10 and R1 get hot too (when on mains), which makes sense, because by my calculations, they're dissipating around 1w of power due to the internal zener of UC3843.