We got some information from a Ranger who told us to avoid the eastern route from Corral Valley road and take another route more central. She told us of a place to stop as even serious 4WDs got stuck regularly is deep sand right past that. I don't remember exactly where but we started on her "safe" route and almost got stuck in very deep sand within the first half mile. I really had to motor through it, sort of over a small hill. So we ignored her bad advice after that, turned around, floored back over the nasty hill and parked on Corral Valley road.
I'm glad we did. It is right at a 10 mile cross country hike from there but we found a literal treasure trove of things that drivers will never see. We carried all the water we would need and camped at White Pocket, a super fine thing. I think I remember water at Red Pocket on the way, a cool old cowboy place. We stayed away from the roads the whole way and did a loop. We always do things like that, hardly ever driving up and photographing the iconic spots and leaving. Cross country has always paid off, very tough...yes, of course, but we always take the long way home.
You can get a very fine visual on White Pocket from way out, lose it when you dip down and reacquire it once more when you ascend the terrain. The Paria Plateau is a magic place and you will see so many things, landscape wise, ancient artifacts, very strange Moki stuff (marbles galore, peanuts, surreal splashes, raindrop pieces and even the occasional Moki hand grenade and cannonball. Some very good lithics, projectile points as well as painted pot sherds are out there as well as some kind of ancient medallions. Please leave it in the living outdoor museum for everyone else to photograph too.

We even found some very good antler sheds, two of them from obviously the same 10 point buck, got some good funny images using those too!
Then there is White Pocket...it is something else, many variations of surreal...
Everything in there is amazing. Yes, it is far easier to drive but...if you are a bit more adventurous and can do a very tough hike loaded down with water, it is a place of its own, very unique...