OK - I think I've managed to resurrect my BM54.
It started with the common high current usage by the audio system, which I had worked around by adding a relay to the fuse 56 feed.
Sometime during my examination/testing, I managed to 'lose' the BM54 completely - wouldn't power up at all, including the button on the HU.
Previously, I'd seen that the DSP amp was being kept alive (by the BM54).
The main steps I think brought my module back to life were:
Really clean all the contacts on the back of the radio module - I used a small wire brush (like a toothbrush with fine steel bristles), then contact cleaner (brake cleaner seems the same)
disassemble the module (take the cover off) the module and clean/check the PCBs - the upright power board was pretty manky, so I used a soft brush and contact cleaner.
I used a loupe to look at the boards and found no significant corrosion after cleaning and no obviously overheated components or bulging capacitors, or broken tracks.
Checked all the radio fuses - I never realised the radio uses fuses 25, 43 & 44 in the glovebox - one of these (43, I think) switches the radio on, when the volume button is pressed on the HU and had blown.
Everything is now working and the current draw issues have stopped - the audio system draw now does the 2-stage shutdown, along with the car
I'd like to give a BIG shout out to RichardP on here, for advising me and putting up with my inane questions!
Also for giving me this REALLY helpful detail on the radio wiring:
Permanent live is the Red wire with Green stripe (pin
Switched live is Purple with a White stripe.
Ground is Brown
iBus is white with little yellow bands every so often.
I'll try and update this thread if things change.