Just to draw a line under this one, in case anyone in the future stumbles across this post...

After looking at how the thing was put together, it just did not look practical to take it apart at all easily - at least, not in a way that was likely to work again afterwards. A PC board that is fixed to its supports via around 4 dozen soldered pins (of which about half were bent over so that there was some kind of mechanical support) isn't the most maintainable item in the world and the chances of breaking a track or two were high. However, by looking at the simplified internal wiring diagram in the data sheet and a lot of inspired prodding with a test meter, it looked as if there was a problem with the internal connection between the 24V supply and the terminal feeding the e-stop switch chain. There is an internal (current-limiting?) resistor and diode shown between these two. I can only guess that these are protective measures in case of external wiring problems. However, my 24V supply is current-limited anyway, and as the e-stop supply terminal and 24V power terminal are literally next to each other on the relay, I moved the e-stop switch chain connection to run directly off the 24V feed rather than via the internal diode/resistor. Problem solved - all works as it should now.