Mission accomplished. I looked at the top and never even considered looking further to the legs.
(Disclosure - I do not care for this piece... at all, but I am always admirable of people who stretch their skills and invest their time and talents into non-traditional designs. Kudos to you.)
I think you left out some words here, like maybe "...that you cannot make any change to the burl pieces shape."
If that is the case, I would have turned to the lathe to make good use of the burl.
If you meant to say "...that you are only allowed to make any change to the burl..."
I probably would have cut it up into same sized square blocks, sliced off veneer pieces of each square, and made about 8 rectilinear tables out of it.
Todd