Hi Again;
Excellent progress thanks to Census Cazay found and your extra work on this.
George Beard age 28 was of Wilts according to the Lady Hodgkinson Passenger List. Ordinary Seaman.
That and the 1841/1851 Census and children George called Jemima and Elizabeth in Australia, seem pretty conclusive to me.
FreeREG has this extracted record, probably George Snr;
George BEARD, Baptised 25 November 1804, St John the Baptist, Pilton, Somerset
Parents, GEORGE and BETTEY
And this is Marys from FreeREG

Mary Wallington BEARD, Baptised 04 May 1834 , St Peters, North Wootton, Somerset .
Parents, GEORGE and JEMIMA
Abode, N Wootton
Father, Blacksmith
Others you can check on FreeREG;
William Tilly BEARD, 17 June 1832 ( May have died as 1841 has a Wiiliam age 3)
Elizabeth White BEARD, 15 May 1826