I discovered that the Brightman, Sir Edward Paget, Kelso, Cheapside, Agricola, Earl Grey and Woodlark left Sydney in December - so too late to reach the U.K. in time for the family to be on board the Childe Harold on 17th/19th February. The Ganges and the Seringapatam also arrived UK past that boarding date - their transit times being respectively 142 and 135 days - so not as fast as the advertisements would suggest.
Back to the drawing board!
Alternatives:
While Richard Bruce was discharged from his regiment on 31st October - could he in fact have left the colony before the date of discharge? I need to get back to the National Archives, Canberra to check his payroll details for the end of his service with the 11th Regiment. Won't happen quickly.
The family left from a port other than Sydney which means factoring in extra travel time.
Both.

Thank you all. J