Likely I will wite a blog about my exact position about AE, "orthodox" and alternaviks, as I suspect there is a clash of cultures and some misunderstanding here....
I do not think we should regard the Dream Stela as an historical document. That's not the purpose it served for Tuthmosis IV. Alcibiades's earlier point about Tuthmosis VI's separation in time from the Old Kingdom is valid: people living in Dynasty 18, royals included, would've known very few real facts about what had happened back in Dynasty 4, a thousand years earlier. Histories were not recorded, fact-checked, and stored in a manner similar to what we take for granted today. This is why I sided with Alcibiades earlier.
At the same time, however, what Tuthmosis IV recorded at the end of the stela is significant. Fortunately Karl Lepsius carefully drew the monument in the nineteenth century, before it deteriorated further. The bottom several registers were already in a fragmented state. I have Lepsius' carefully rendered drawing in my digital library, and although the name of the king in the cartouche near the end is badly damaged, there is no mistaking two glyphs: N8 (sound value xa) and I9 (sound value f). This produces xaf, "Khaf." I can't think of another king with this arrangement of glyphs in his name, so there's no sense in arguing against the fact that the name in full was Khafre.
That said, while I don't regard the Dream Stela as an historical document, it's clear that Tuthmosis IV himself regarded the Sphinx as the work of Khafre from Dynasty 4. We can confidently state that much.