What you've described sounds a lot like x264's --crf option, which adaptively chooses a bitrate based on the input. How is Beamr different?
I'm no expert on this matter, so apologies if this is a dumb question, but: has the perceptual quality measure used in CRF been subject to the same ITU BT.500 testing?
If it hasn't, then I'm afraid your case remains unproven.