There are a couple of access points down from Potash I believe, though most or all require rather involved/severe 4wd, and some are really not practical (miles of hiking to the river) which is why everyone just uses Potash instead. Not worth the trouble?
What I've heard about put-ins below Potash:
You could look at driving into Laythrop (spelling?) which comes in on river right. I sometimes see jeeps there, and it's popular enough it has a composting toilet there by the river.
I know there is 4wd access into the maze near the confluence (atop the canyon), but then you'd need to hike the rafts and gear several miles downhill to the river (i.e. not worth it). This hike is strenuous, potentially sketchy, and possibly exposed without a backpack, let alone hauling gear. Would be much more dangerous than the rapids. This is also on river right.
I heard someone mention the other day that there may be a 4wd trail near the confluence on river left..
I recommend simply sticking to Potash.