I suspect a diamond speaker works along the same lines an an open backed guitar amp cabinet. There is some bass attenuation, varying depending on what's behind the speaker. That's what I use (open back, 12 inch speaker) for both theremin and guitar. My bass amp has a ported box.
Notice on Peter's video with a naked speaker, he has a microphone stuck right in it's face, so the recorded sounds should be a bit more full range.
I'd try your Fostex speakers and see what happens. All you have to loose is a bit of time and a small amount of plywood.
A Peavey BW, while a great speaker, would probably be overkill here.