You need to go to the red rock four wheelers web site to see if there are any runs still open during the safari. If there aren't you can still go and just show up at the city market in the morning to see what folks are running trails outside the safari each day.
As for an RV space, you're probably out of luck there, most folks make their reservations no later than January, but there may be cancellations. As for camping outside a formal park, BLM campgrounds in the area are a first come first serve basis, you can camp in the desert areas for free, but you certainly won't be alone during safari week.
It's a fun event, but most people get RV spaces months (or a year in advance) and register for runs on the first day that registration opens online.
Do a little searching online and see what is available, it's a fun week to be in Moab, Happy Trails!