As usual an interesting OP cram packed with information. Which can (has) lead to much thought and side reading, which is likely beyond the scope your intended specific focus.
It appears it is a scholarly question focused on minutiae, based on or incorporating a lot of the presumptions of established Egyptology. ( Albeit, I realise you do not necessarily agree with many of its tenants)
In focusing on that minutiae some points come to mind:
Another alternative is that the lid or “the greater part of it” found by Vyse separate area to the lost sarcophagus belongs to a different intrusive placement at some unknown time.
(It is clear that in Vyse team was a gifted artist. Note the effort to incorporate shadow from the torch held. Given the skill and beauty of the drawing it seems to me it is likely a very accurate rendition of what they found.
Whether the same artist drew the poor elevations and plans is somewhat questionable. )
On a broader perspective your thread highlights many inconsistencies inherent in the guesswork and chain of Chinese type whispers that conjures up mainstream understanding of the various Kingdoms and Dynasties.
There is not any consistent “sarcophagus” style of the 4th dynasty or OK. If we just focus on the pictures of ‘sarcophagus’s” you have presented. We are led to believe and accept that in the space of four generations that:
- Snefuru or the “ intern” in Meidum opted for a rough unpolished granite box with an ill fitting lid. The lid similar but of much poorer finish to the “style” of those evidenced in the attributed to a much later NK Serepeum.
- Son Khufu, the most specific and demanding particular “pyramid builder” of all time, opted for a plain undecorated relatively smallish granite box. The seal rim rounded and rough, but the interior beautifully smooth.
- Grandson Djedefre , (or someone buried near Abu Roash) wanted a beautiful alabaster (or limestone?) box decorated with the prominent intricate “building” or doorway pattern. However opted for a totally inconsistent poorly finished rough lid?
- Other grandson Khafre, reverted to one like father Khufu, just a plain granite box, but thought it better to produce a squarish better fitting lid, sunken in a stage.
-As an aside we are also asked to believe that despite his relatively modest taste in sarcophagus, his wife Meresankh III deserved the decoration of the “building” or doorway patterns of those of the unknown epoch folk. ( Note extremely difficult to achieve in hard stone, and impossible with only copper tools/chisels )
- Then great grandson Menkaure decided to go the whole hog on the wonderful elaborate “building” or doorways pattern with a few extras , if Vyse is to be believed in BASALT! He surely knew what Basalt was, as distinct from Alabaster!?
- To top it off, the elaborate “building” or doorways pattern box is not only found in the Eastern cemetery of Giza as the picture you “dug up” shows, but there is a similar one, seemingly abandoned , in a corridor under Djosers step pyramid!
My purely speculative amateur (perhaps ‘fresh thinking”) conclusion that over the ravages of many millennia of the AE civilization, and subsequent two millennia of post AE period that sarcophagus have had lids smashed and replaced mismatched, stolen, moved , reused, and we can’t possibly in most cases know when!
Regardless, Menkaure's sarcophagus as depicted by Vyse seems incongruous to the time. The question is why?
My suggested answer is because of the confused, illogical, inconsistent, incoherent, incongruous perspective that mainstream Egyptology has cobbled together of what is thought/guessed/presumed to be congruous to the “time” by which I think you mean Old Kingdom and perhaps more specifically 4th Dynasty.
This is made abundantly obvious by the short written rant of Hawass posted by EoH!
Please forgive, or ignore, if off topic or seemingly irrelevant.