I traced bcmsdh_sdmmc back to bchdhd using the lsmod command, which some googling appeared to confirm to be correct.
I then simply added bchdhd to the bottom of the /etc/modprobe.d/blacklist.conf file as:
blacklist bcmdhd
Rebooted and so far so good (although obviously no wifi)…
Thanks to @smlikens for the tip 