"Ironically the 5D Mark III is a great (or at least good) body with a mediocre sensor."
Ironically, its predecessor the 5D Mark II was the other way round.
I don't think so. The sensor of the 5D2 was simply so good that only minor modifications were necessary.
I somewhat agree with you that criticism of the 5D3 sensor is a bit exaggerated: the 5D2 had, for its time, a great sensor (maybe even better than that of the well-received 1D3) at a good price, with the main weakness being that Canon cut a few too many corners elsewhere in the body, especially when compared to the D700 and A900 that arrived
at about the same time. So Canon's priorities for the 5D3 were understandably along the lines of offering an ”EOS 3" class of body with things like improved AF and VF, which now are Canon's best, not its second best. Oh, and improved video.
But there is one respect in which even that sensor's being "state of the art" when it arrived four years ago is very different from "needing only minor modifications": it was well-noted even then that for some scenes of high subject brightness range, the 5D2 (along with every other sensor in existence then!) could fall short, to the point that this was the one aspect of performance where digital still trailed film, or at least required more careful handling than with film. So Canon's failure to progress in maximum dynamic range is not fully justified by the claim that "only minor modifications were necessary". At least not in a model that is the highest resolution offering in the entire Canon system, and so the best Canon option for some photography of landscapes, architecture, and such.
By the way, it seems that you too have offered your own 5D3 mini-review; all this forum user feedback is even more reason for Michael not to do a review!