Since you're in a corner, you can definitely pull this off. Structurally it reminds me of a knee wall with a wall at its end like the knee wall from How can I anchor a knee wall to my basement slab?. The corner location makes your design possible. Rather than traditionally oriented framing, though, you would implement a diagonal cantilever. Consider

Basically you have a cantilever. One end is supported at the corner. Then there's a midspan support at the band of wood connecting the two walls (the dashed region from the drawing). After you fill in the load conditions a little better, it would be pretty easy to figure out sizes. The tricky bit would be reinforcing that band of wood connecting the two walls so that it doesn't sag too much under the 400# midspan load.
Glue together a couple pieces of 3/4" plywood to form a composite 1-1/2". That'll be plenty strong and stiff as long as you get your wall anchorages right.