Agreed, the children's papers would be very informative. Unfortunately this would require a visit to Hobart in person!
I note there was a Frederick BURDEN with wife 'Lizzie' in Nubeena - he died in 1921 aged 48. Any connection?
It seems curious to me why all but two of the children were taken into care after the death of their mother in 1915. Effie who by all accounts would have been 14 or 15, and David born c1904 (if the shooting accident at age 18 was him) are on that records list. But Arthur & Clarence, the two who seem to remain with their father, weren't the youngest (Arthur was born c1905).