I think what's going on here is pretty clear. The noise clearly originates from your BBE power supply, which is evident from the fact that the problem goes away with the 1-Spot. Apparently, this noise is filtered out by the overdrive stage of the CJ when it precedes the boost stage. But when the boost is first, it amplifies the noise to an extent that it's audible through the overdrive circuit. I would definitely try what Morgan suggests, but if that doesn't help, I'm not sure that there's much you can do about this other than not powering the CJ with the BBE P/S.
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