Am I stupid to even contemplate using both?
Nope, not stupid, just potentailly poorer without benefit. But, that's pretty much the risk you take in anything.
I tried all sorts of power conditioners with mixed results...until the BPT-2 came into the picture. I only tried a $139 auto voltage regulator from Best Buy and it degraded everything (hardly a good test of AVR's tho).
I
think it's voltage regulator first, then power conditioner. You may want to look over
www.furmansound.com and see if there is guidance there.
They make both, so they might lead you the right way.