Have you tried airing down the tires:
    http://www.4crawler.com/4x4/PismoBeach/index.shtml#DrivingInSand

I have driven my GMC 2500 conversion van on the beach a couple times.
Once in Mass. and once in Florida.
The sand in Mass. was wet and packed and was easy to handle. The stuff
in Florida was loose and dry.
I am running Liberator A/Ts from Wal-Mart on it (cheap but decent
rubber). I aired down to 20 psi and drove around a bit, The key is
Momentum, lose it and you will stick like glue. IF you need to stop you
can keep from sinking by driving onto harder sand OR
carry something to park on (I used some old carpet and a couple of 4x4
pieces of plywood) to spread the weight.

A few years ago, I read a tire test article. They went to Baha in a
Scout with several types of tires, and had to keep digging it out.
Meanwhile the natives were driving around in their 62 Chevies with
bald tires.  
You want high floatation tires that don't dig!
Dan

"Is there anything I can do besides a 4x4 conversion that will make my
4x2 full size G20 van make it through some pretty thick/sinky sand?"

Pardon the generic quoteing, i use aohell...On my toyota two wheel drive pickem
up i fashioned a poor mans set of turning brakes to deal with sand and
gravel/shale traction issues. Installed 2 levers right behind my floorshift.
From each lever I ran a cable to one side of the factory sock emergency brake
cable and used a cheap cable u bolt clamp to join the new to the old. When my
spider sense told me i had a wheel spinning and hence one sitting powerless, i
simply said "wondertwin powers etc etc" and pulled the spinner side brake while
keeping steady on the gas. Diff took over and supplied power to both wheels and
many problems were nipped in the bud. Of course, like anyone in Az will tell
you, expect bs cause it happens. Carry a nice big sheet of longer stranded
astro turf with you. You get stuck instead of digging your self in further,
immediatley lay off, put her in nuetral or park and place your turf mat in
front of your rear wheels with the grass side down.( Leave  buddy behind to
grab the rug, cause you'll prolly need it a few yards or so later,) get in and
drive outta there, using the po boy turning brakes as a traction aid.
That in combination with air ing down and you should be set. Save ya a whole
buncha dinero over the locker / big tire setup.
And like inspector columbo always said, just one more thing.....
I never tried it , but I always thought of using tire chains , kinda like
paddle tires at the dunes.......might happen....coulda shoulda oughta
work....yeah, thats the ticket........
let us all know how it works out.......
MLM