I've been out there a few times, and you are definitely correct that it is far more rewarding photographically (and in other ways) to stay overnight so that you can experience sunset, night photography, and dawn light on the playa. (You are a brave person to have driven that road at night!)
The official word on camping is more or less the following - but double-check with DVNP for accuracy and details... There is a small "camp ground" a couple miles beyond the south end of the playa. It is little more than a couple of pullouts and a very crude outhouse. There is no water whatsoever, though there might be a table or two - I don't remember for sure. It is a very quiet and peaceful place to camp.
If you camp there you have to drive (or walk?) back and forth to the playa to do your photography.
People do sleep in their cars alongside the playa. I'm not certain of the technical legality of this, though it is hard to imagine how it could do any actual harm as long as you practice leave-no-trace sleeping-in-the-car camping. This is a more appealing option since you wouldn't have to travel back and forth between the "campground" and the playa - especially since you'll likely want to shoot until or after dark, and then be out on the playa and ready to shoot again very early in the morning before the sky begins to light up.
When I've been there I've actually gotten very little sleep. Here's an account of last years visit: I arrived at the playa in mid-afternoon and discovered that this can actually be a very interesting time to photograph The Grandstand. (It is in shadow later in the afternoon.) After shooting there I headed toward the south end of the playa and took only a short break before trundling on out onto the playa for several hours of shooting as the light went from afternoon to post-sunset. When it finally got fairly dark I headed back to my car to get something to eat and take a break. Because this was a full-moon night I then headed back onto the playa for more shooting and kept going quite late.
I finally did get a bit of sleep, but I was up very early again in the morning since I wanted to already be out on the playa before the light arrived. The light interest goes through several phases in the morning, beginning with the very early pre-dawn light. Then the sun begins to strike peaks to the far west and then just west of the playa, and also to the far north - for the latter you would be shooting across a relatively darkened playa surface with well-lit peaks and sky beyond. Eventually the light begins to shine across the north end of the playa, working its way gradually south to the part of the playa with the most sliding rocks. A very magical moment is as the light boundary travels towards you and the playa goes from shade to relatively low angle light. There are actually some rock trails that are invisible until this low light hits. (The only thing more magical is when there are clouds above the playa on a windy morning and the cloud shadows race across the vast surface. To die for...)
Climate out there is variable. It can be quite cold at night, so do bring warm gear - clothes and sleeping bag. I've seen snow in the vicinity. It hasn't rained on me when I've been there, but it could happen.
There is a good chance I may be there around the very beginning of April this year. Email if you want to try to meet up.
I am headed to Death Valley in April. I've previously photographed at the Race Track from afternoon to sunset, driving back to my lodging in the dark.
This time I am considering camping overnight at the Race Track to catch the early morning light. I am very interested to hear the experiences of anyone who has done this and any tips are greatly appreciated.