What can I add to veggie burgers to make them less brittle?
Wheat gluten.

Buy some powdered wheat gluten at a health food store.  Add it to the mix, add some water if necessary, and stir it around in the same direction for 30 to 50 strokes.  The gluten will bond and start forming long chains, and bring the whole mixture together.  Nothing else really works as well.

Eggs and cheese will also help hold a veggie burger together, but only gluten really gives it cohesiveness and a springy texture.

FWIW, I can't imagine that veggie burgers made from juicer pulp will be even remotely appetizing.