Ended up downgrading to 6.0.3 here (well, installing a new appliance from scratch) and haven't had any problems since, running a 0.5TB store with the default 4GB RAM.
I've come to the conclusion that out-of-the-box 6.1.x is a dud release so hopefully whatever the problem with it is will be fixed in a future update. Chucking even more host resources at the VM for what seems to be a minor update isn't very appealing...