I can now confirm that you can not do this. Fortunately after an epic hold on the phone the officer agreed to prioritize the cases and within 2 days they were both approved.
The fact my own Hong Kong work visa, and my sons as a dependent, were ending on or shortly after my resignation date in Hong Kong and we had put notice in on our property, along side an early December start date, probably helped persuade them of the urgency.
In hindsight I would have done this differently and not relied on a priority request.