This is thanks to Stuart Tyler and his Hatshepsut Project at
Perhaps because the fragment rests in a rather obscure Scottish museum, I had never viewed an image of it and was so surprised and appalled that I asked Stuart if there was any possibility it might be a fake. You can see my conversation with him, as well. But he convinced me it was not and I then realized that, at the time of the building of Hatshepsut's mortuary complex, [ca. Year 7] Thutmose III was supposed to be out of the picture entirely. He really had lost his throne to Hatshepsut's ambitions.
They were not joint rulers at all or Neferura, Hatshepsut's daughter, would have been displayed as a mere princess and not with the diadem and sidelock of an heir apparent--yet another female pharaoh waiting in the wings. During my conversation with Stuart at his site, you can view the URLs to some images of Ramesside Era princes wearing a nearly identical diadem and sidelock.
[click on image for larger view]
There is nothing in existence depicting Thutmose, himself, as a prince. It is scarcely any wonder, then, in light of the above image, that William Petty, in a couple of articles, has pointed out that there are no unambiguous inscriptions of Thutmose III between his Year 5 and Year 13. Where was he and what was he up to? But, sometime after Year 13, Hatshepsut changed her mind and Thutmose began to appear with her on monuments albeit in a secondary position. Then, in her Year 21, Hatshepsut, herself, becomes absent from the record. Under the circumstances, I have to agree with Petty that Thutmose found it convenient to continue the last regnal date of the woman-king. He may have been the rightful sovereign, but it now seems to me he had been deposed, not merely eclipsed, and was not expected to ever resume his kingship during a certain period.
William Petty's paper in the journal, Ostracon, "Redating the Reign of Hatshepsut" can be found here:
There he gives an account of the items dated to the years of Thutmose III and Hatshepsut, finding a gap of seven for the former.
Addition of October 30: There is however, the problem of Thutmose III being depicted at the mortuary temple of Hatshepsut. According to Alberto Siliotti, construction of the temple of Hatshepsut took fifteen years, between years 7 and 22. Here is where I hit a limestone wall because I have no way of knowing if the depictions of Thutmose are contemporary or retrospective. For example, he is present in a scene commemorating the famous expedition to Punt in Year 9--but in which year was the scene executed? Probably not until at very least Year 10 and by then a co-regency may have been restored. Since I am not familiar with the stages of Djeser Djeseru, I can say no more until I have done more research on the temple.