Thank you all for your suggestions. In the end I used several techniques and the board has now been recapped.
I played around with a couple of PCBs:
- a 1972 PCB containing core memory,, fine tracks, double sided PTHs and old(!) solder
- an ATX PSU, ground planes, single sided
As predicted, the cheap heated 40W solder pump was a little fierce for my comfort. However, running it from a variac and reducing the voltage by 15% also reduced the temperature by ~15% (not 22.5%?!).
The Chip-quik bismuth solder might have formed alloys that reduced the required temperature, but definitely had the benefit of providing a good thermal contact at a relatively low temperature.
The heated desoldering pump was good at quickly removing the solder used for large snap-in capacitors. That was mainly because there was a lot of solder in a large hole, and once it started sucking into the pump, it all ended up there. The vacuum on its own is only partly helpful at removing the solder; equally important is that a strong draught into the pump picks up solder and removes it. Hence melting the solder and then holding the pump tip at an angle (to allow a draught) often worked best.
None of the techniques were excellent with small holes and closely fitting leads. I tended to use the pump to remove as much as possible, then desoldering wick with flux.
Sometimes that left a difficult-to-shift solder bridge deep in the hole. Tthe best technique was to melt the bismuth solder and allow it to flow into the hole. Then it could transmit the heat to the lead solder, and both could be removed with a wick.
The three legged capacitors are unlike anything I have seen. The third "axial" leg is just the can, and that is insulated from both the other terminals. I wondered if that is to allow some extra shielding connected to the ground, but that doesn't seem to be the case.