Las Vegas area late March

We prefer provincial/state/national parks and my research has found that most, if not all, of those facilities in the LV area are "first-come - first served".
We hope to be in the LV area at the end of March/beginning of April for the world men's curling championships and the NHRA race.
Is it realistic to hope to find a spot in one of the parks in the area or should we just bite the bullet and reserve a spot in one of the commercial RV parks?

TIA,

Tim & JoAnn