A fellow descendant of the Trevithick's sent me a copy of their arrival indent - one of the few records I was missing. I'd always hoped that the record would reveal his parents names and other details (as NSW arrival records do), but the Victorian records are relatively spartan.
The 'Panama' sailed from London on 3 Aug 1854, a ship of 734 ft, carrying 275 migrants, arriving in Portland on the Victorian coast on the 25th October 1854. After they set to sea, Elizabeth gave birth to the first of their ten children, Elizabeth Trevithick.
Their arrival record image:
TREWITHICK ----INFANT WITH I OCT 1854 PANAMA
TREWITHICK ELIZH 21 OCT 1854 PANAMA 10
TREWITHICK THOMAS 21 OCT 1854 PANAMA
It's easy to see how the name was mis-stranscribed! Based on articles and even headstones, it appears that that 'th' in TREVITHICK was often heard as a 'hard T' sound, and perhaps the v was softened to the point that it sounded as 'trewitick':
Here it can be seen that Thomas stated his occupation as a blacksmith of Cornwall, listed with his wife Elizabeth and a daughter 'b.o.b.' - born on board (registered in Victoria on arrival, who we know to be Elizabeth).
The arrival record also reveals that family to be 'Church of England' (Wesleyan was an option but they didn't claim it). Both Thomas and Elizabeth claimed that they could read and write, and both were 21.