I've got this almost licked.

I took usps.php and hacked it up to make a new shipping module that take into account the flat rate box volumes. I also added a product_volume field in the products table and made sure it got added up in the cart. This module only quotes flat rate options. I use it in tandem with the original usps module.

Since I have a shipping volume per product, I can figure out which box it/they can go in and submit the quote accordingly.

It's not ready for prime time. I'll try and find a spare weekend when I can clean it up and post it.