one of which holds more fuel than the other so that both engines don't run dry at the same time.
Theoretically it does, but with fuel able to slop over the divider between the two supply tanks the time between both engines running dry is, in reality, indeterminate. You could have both engines flaming out together. Bad design.
Where in the check list for a double engine flame out does it say switch the SHED BUS to emergency - if you can find it?
DV