Lighter weight than Buckeye Burl (which fills up with a bit of dense polyester finish) would be Lacewood or Koa. Lower density means a more mellow, rounder tone.
The biggest difference you can make in the weight is the choice of neck woods. Using Mahogany as a primary neck wood will certainly shave an amount of weight away that anyone, even without a compression injury, could appreciate. Again, you're looking at a more mellow, rounder tone compared to Maple. To brighten it up some, you could counter with stainless steel strings, and we could tune the filters higher so you can get a more extreme upper end (maybe 8K or so).
Walnut's unique characteristic is to impart a quick attack, at least when used as a top on an Alembic bass with a primarily Maple neck. Some of that attack is preserved on a Brown Bass, which uses a Mahogany primary neck wood, but it's not as dramatic as with a Maple neck.
It might be useful to get opinions of some folks that have used both Brown Basses and other Alembic basses with Maple necks to see if it's something that would suit you.
One other way to save weight --- reduce the scale length.