facsinating read last night of the Roma Dulhunty book. With cross referencing to current websites, Ive made a few observations
she frequently mentions the winter winds, but no direction!
The interesting bit , the Peninsulars , is out of bounds to the public-thats us! This would need to crossed or rounded to the north end(the slush zone).
There is no public access across Goyder channel so your access on the east side of the lake is very limited with NO camping allowed.
Rita's outback guide says that driving on the lake is an offence, The SA dept of Environment and Heritage says it is extremely inadvisable. perhaps somebody could confirm the offence bit for us

Access on the west side is Via Oodnadatta track and William creek, so youd need a fleet of drivers to get vehicles to the other end. the access is to Halligan bay, way up on the red clay, north of the slush zone..
With all this in mind I think you would need at least 1 4WD quadbike with trailer as a basic support for your Kite Buggies. I think that a Landyacht attempt would be inadvisable.
Basically in order to attempt a landyacht crossing , you would have to tresspass on at least 2 stations,2?national parks, be committing vehicle offences for your yachts and your support vehicles.
sorry joe , but I would be a no on this one