If you were actually considering crossing the lake . here are a few things to consider.
virtually all the edges will be soft and sticky . big fat smooth balloon tyres will pick up many times thier weight, tall skinny tyres will sink , but the taller the better. they should be very light.spoked wheels will pick up mud.
landyachts dont sail very well on soft mud, if you are lucky they will slide sideways.
I would be seriously thinking Kite buggy towing a trailer. maybe a trailer that converts to a landyacht on the offchance that you find some hard salt? the sail could be designed to double as a shelter.
it would be worth building the body to give some kind of floatable shape and capacity because if it rains on the lake the water blows up into small moving lakes, which although probably shallow, you and your gear will need to be able to get up off it to stay dry.
as some training sessions I could suggest that in NZ you go find a really smlly muddy tidal flat and drag you yacht and gear up and down every day for a week( camping each night).
In Aus , Im happy to drop you off at one end of Lake Lefroy, with a map, gps phone and gear, and pick you up at the other end each day for a week
please note lack of smileys in this post
keep in mind that all this gear and your food , water, extra water, shelter pare clothing........... needs to weigh nothing as you will frequently have to drag it across kilometers of mud. youll need extra waterfor cleaning youself each time you do that. lots of antibiotic creams and salves for the cracking flesh etc