Unsure about snakes. We didn't see any on our trek in July, but this'll be at about the time when they'll be getting active so I'd plan for a yes on the snakes. I'll be taking my swag and that's about all as far as sleeping arrangements go.
My plan would be to do the races on Friday and Saturday, allow a 2 day trip to the corner and back (camping in the desert is pretty awesome!) be back in Birdsville on the Monday, then head off down towards haddon corner and innaminka try and do Cameron's corner while we're at it. Arkaroola and flinders ranges maybe, then head back to brissy via broken hill, dubbo, etc.