For posterity, the problem was initially solved by changing the switch between the two CARP members.
Apparently the Aruba-flavoured HP switches call home ( to activate.arubanetworks.com ), and while I'm not sure why this wrecks things for a multi-WAN CARP setup, once the feature was disabled on the switch it ceased causing STP problems.
We only found out because we had to replace the (replaced) CARP switch in a hurry (next planned setup will have redundant switches too).
The guy who arrived first grabbed the first unattended switch he could find (it was the HP), without knowing the problem it initially caused, and was just happy to have it already configured with the correct VLAN groups. Asking around, it turned out the only change in configuration was the mentioned call home feature being disabled.
Hope this helps someone. It had me banging my head against the rack for way too long.