I don't see why you consider proprietary relicensing as a requirement for Open Core. Indeed, it appears to me that you regard Open Core as covering even the practice of selling exceptions, which is explicitly excluded from the definition by both Aslett (downstream from Lampitt) and Mickos (upstream).
Linux and GNU/Linux distros have shown us that relicensing of the Free core isn't always necessary to offer non-Free add-ons to go with it, together or separately.
After all these discussions, I must agree that Open Core is understood in different ways by different people, but I'm not sure how much of it is a consequence of the way the definition is phrased, how much is just the normal sort of communication partnership in which different readers get different messages from the same text because of different personal backgrounds, and how much follows from the common twisting of meaning that we so often see term such as Free and Open Source undergo.
In retrospect, I'm very happy we used a different term, Free Bait, implicitly defined as equivalent to what we perceived and described as Open Core. It might be wise now to publish a stand-alone definition, independent from that of Open Core. Since our understanding of the meaning of Free Bait won't have changed, it's clear that Linux and GNU+Linux distros will still fit it, and that the deceptive practices of passing non-Free (or partially Free, as some prefer) for Free Software will still be subject to criticism, but it remains to be seen whether the criticism from third parties to the Open Core practices (however they understand them) will be sustained or retracted when it comes to Free Bait.