If I understand you correctly (which may not be the case) you are suggesting a test where during the 16 (or however many) iterations you might change either a cable or something else.
Whilst it might be counter intuitive, such a test would not really prove anything unless a far larger number of iterations was used in order to make it statistically significant. It also makes reaching any statistically valid conclusions very hard.
I don't see how my suggestion of ABX-ing some cables and then ABX-ing some boxes (or the other way around) wouldn't just as validly test the same things - provided of course that the test subjects don't know whether cables or boxes are being tested.
The results you'd get would be: cable A and cable B could/couldn't be told apart and separately, CDP A and CDP B could/couldn't be told apart.
If I'm "right" then the CDPs should be distinguishable but the cables not. The test, in order to be meaningful, has to of course involve more than just me as a test subject and the results all bundled together allthough looking at how different individuals scored would be interesting.
Michael.