Instead of going deep and heavy, why not go surface and light.   Spread wide 
with a big long strong plank with the cable attached in the middle to a 
fitting that will cause the plank to sit at an angle to dig into the sand 
when pulled, a little like a wide plough.   Think of it acting like a sea 
anchor.   Might even splay out several cables from a ring at a come-along 
half way between the boat and the anchor plank, the cables to distribute 
load to the outer ends of the plank as well as the centre.

If the sand is dense and water packed, then more of a blade will be needed. 
If it is loose and fluffy, then the plank will do.   You really don't need 
that much power to do the job.
or
Maybe a half dozen long tined pitch-forks would provide enough dig.
or
If it is windy there, get a big para-kite with two control lines and let it 
pull your cart.

cp in bc
(dedicated stunt kiter) 

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