EDIT: entirely new answer based on comments
You may actually be on to something here.
The most obvious (and thus least interesting) answer is that they were
depicting Orion shortly after sunset, not shortly before sunrise (all
times UTC):
Here is the helical rising of Orion today, and it does indeed go right
to left:
If we go back 1000 years, it's much closer to being a straight line:
And if we go back to 1473 BCE (which is -1472), the rising is clearly
left to right:
Interestingly, if we go far enough south, the rising is right to left
even in -1472:
Note that position in which Orion rises doesn't change much from day
to day. In other words, the position of Orion's stars at helical
rising are the same as the position of Orion's stars at rising any
other day of the year. Because of precession, the position does
change over long periods of time, but not day to day.
The only problem with the "most obvious" answer above is that we know
the Egyptians were very interested in helical risings, so it would be
odd to see a depiction of a "helical setting".
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