I know you have a very specific way to train, so don't hate me for this, but have you heard of the so-called earthquake method? Basically you shake the crate when they act up and it's "scary" enough that it makes them stop. It's supposed to be pretty successful.
I didn't have to make that decision -- that was one issue we didn't have -- so I don't know what I'd do. I can say that Grace's "I'm done being in my crate now" screaming can make me feel like my ears are bleeding, and it's not even when I'm trying to sleep (which would make me even more irrationally angry at the world).
Puppies are tough! At least mine have been... At least you have adorable pictures to look back on and you'll magically forget how hard it was.