Well guess what, 10.31 of the switch firmware has come out, and they have added this really important feature:
"Ability to download diagnostic data about the device from the local status page"
It appears under "Uplink Configuration" and looks like this:
It produces a file we can't do anything with - but at least when a switch has gone offline and there is no way that support can help - you can now generate a support package for it to be looked into further.