We just crossed the Simpson recently (10 4wd's & 18 months of planning) and these are my thoughts (if you don't agree please be nice).
First off I was somewhat surprised (and even perhaps a tad disappointed) that the trip was not more challenging - maybe the trip is a lot easier these days as lot's of people are doing it or perhaps I had built this up (in my mind) to be a lot more demanding than it really was - after doing that trip I believe that a half competent driver in a stock 4wd (in good condition) should have absolutely no problems doing the trip. I think that you could comfortably cross the Simpson in a stock D22 - west to east should not be a problem - east to west may be more of a challenge.
My father in laws car was 3 weeks old with nothing at all done to it (Hilux) and it did not look like have a problem or getting stuck
I think you could easily spend around $5000 and have a well setup car for the trip - I would do the following (but honestly think you could get away with only 10 & 11):
1: Long range fuel tank - as large as you can fit.
2: underbody water tank.
3: Raised suspension (ironman or something similar) - 50mm would be fine.
4: stronger shocks.
5: roof racks (but only to store your light stuff - bedding, tent, clothes etc),
6: UHF radio
7: sat phone (they are actually cheap to buy now and you can get reasonable plans)
8: A handheld navigation unit - we had a cheap Garmin and I could not believe that it was tracking our progress through the desert.
10: underbody protection
11: A good set of tyres
+ a good easy to pop-up tent - we had a 30 second tent and it was good - but it is big and we needed the proper basket for it on the roof - the other option we looked at was the black wolf.
+ perhaps a set of max traxs
I would not bother with things like chips: new exhausts etc - anything that is designed to get you more power - if you want power buy a V8 commodore - in a 4wd you can spin the wheels just as easy with 120hp as you can with 150 - and once the wheels are spinning it does not matter how much power you have.
I would avoid the camper trailer - it could become very painful - I’m not even sure what the story is with Camper trailers in the desert - I heard all these stories and I'm not sure whether they are urban myths, true or just ******** - but I was told that you cannot take a camper trailer through the desert and if you want to you have to pay a bond (in case someone needs to retrieve the trailer) - but we did cross path with some guys that had camper trailers - but these guys were setup - the trailer and the 4wd's all had 10"" lifts on them - they were going east to west and said they were having no problems.
In reality I think you are more of a chance of damaging your vehicle before you get to the desert - some of the roads are a bit rough - some have lots of corrugations which is not a problem unless you get a driver who is not confident on the dirt and they drive too slow - it rattles the car to bits - you need to travel at a good comfortable speed (90 - 100ks).
The deserts the easy bit. But it's a good enjoyable trip.