I'm a life-long woodworker and have built the GRR Super V's, so I wouldn't want to discourage you from building a set. CSS has a good rep and, from what I've heard, yields a well designed product.
While you could use solid hardwood for the side of the cabinets (the width of all four box-surfaces will expand at the same rate)..it wouldn't be advisable to use solid wood for the front and back of the cabs as the expansion will tend to break your box side joints. Gluing up multiple strips of hardwood won't matter, they still expand like a one-board panel.
As far as sound goes..you'd be better off with MDF as it'll be less resonant.
All that said..I've recently seen a used pair of Vandersteen 2Ce speakers in excellent condition for sale at $800. If I were to think of a $650 project (for the hardware..the veneered ply or MDF is $80-$100 a 4x8x3/4 sheet)..I'd pop for the Vandy's and build something else. Try a cabinet with louvered doors..that'll expand your horizon's..speaking from experience.

