travel light, share spares between vehcles, 2 spare tyres, take your time and enjoy. never been across yet , been to both ends and had to pull out for various reasons. Sat up on big red in 2008 and pondered what could have been while watching the sun go down, in 2009 left dalhousie pre dawn only to realise at first stop to watch the day dawn that I didnt quite have enough fresh food (plenty of tinned and dried), had given away more than I realised a couple of days earlier to a strand (broken down) aboriginal family. So the dream is to have a full roast meal out there and I will one day
cheers
blaze
ps
water is more vital than food

We did it in 2006 as a tag-along trip. The sand was very very soft, but slightly firmer in the mornings when it was cool. The nights will be cold camping there, but its absolutely fantastic, you have million-star accommodation!! We saw only a couple of thin dingoes.
Put tyre pressures down, set air vent in your cabin to "intake" to pressurise the cabin and reduce dust ingress. Take spares for everything, but share where you can to reduce your load, and take extra food and water just in case. You'll also need a tow strap and shovel between you!
We had experienced guides with us, (which we paid for) can only say they were marvelous, we thoroughly enjoyed it.

Make sure each vehicle has a dune flag to fly - we manufactured ours from an old aerial and red rag.
Keep your CB on and listen for other vehicles in range - and double check what direction they say they are travelling in. Some people can't tell east from west and we nearly had a nasty meeting at the top of a dune, as a result.
Plan menus that don't need heaps of water for cooking. The usual staples of rice and pasta are not a great idea, for that reason. You need to minimize dish washing up, so one-pot meals are good.
Take lots of baby wipes to save on personal washing water.
Make sure at least one vehicle in the party has a HF radio, or satphone and or epirb.
You will soon learn to tackle the dunes at a speed and gear ratio that gets you to the top - just - because you need to be cautious about what will be one the other side of the crest. The only time we almost came to grief was where some clown had got stuck on way up the other side, dug itself out, and left a huge hole - which we landed in and nearly rolled.
Do not tow anything.
We travelled the same way as you - van in store in Alice, but we went to Palm Valley, along the Finke through Boggy Hole to the Ernest Giles Road, then across the Hugh Stock Route and into Chambers Pillar, then down the Old Ghan Track and across through Mt Dare to Dalhousie. I recommend a camp at Purni Bore - surreal place at dusk and dawn. We used the Rig Road, then came north from that to the Knolls and the French Line and on to Birdsville. We camped at Dalhousie, Purni, alongside the Rig Road a couple of nights, vicinity of the Knolls, beside QAA track - we took our time. It was a wonderful trip and I look forward to a report of how it went - hint, hint.

I did the Simpson on a tag-along in 2001, east to west on the French Line from Peoppels to Dalhousie. One comment to add regards tyre pressures. As well as reducing them for the desert (max 20psi) you'll need to reduce them for the seriously rocky roads around Birdsville.

The tyre "wallah" in Birdsville strongly recommended to us a maximum of 28-30psi. Obviously you'll need to increase them to normal once you hit the black stuff. Tyres ain't cheap in Birdsville as I found out on that trip. If your tyres don't have at least 50% tread life left you'll need to replace them, spares too.

Our trip across the Simpson has been delayed due to an injury to one of the others in our group. Will fill the 4 weeks quite easily and then return to Alice later in August.