OK, I did two tests. They weren't perfect.
-I failed to revolt to slaves before starting the test
-I couldn't get our capital to produce 3

, for some reason after I WBed the copper into it, it stayed at just 1

-In both scenarios, I researched Hunting - Pots - AH
1st trial, no axemen:
I chopped 3 forests. river grass 1e, river grass 2e, then plain hill 1ne. The worker then made a mine in place, then moved to the river grass 1e to cottage. The cottage was started 5 turns after Pots came in.
Pyramids in 17 turns
2nd Trial, 2 axemen:
I chopped three forests, and whipped 2 axes.
After the first forest chop (river grass 1e), I moved the worker to the forest plains hill 1ne. Since the capital started on an axe (with 80/450 on Pyr, 25 turns), I set the worker to mine the hill (8 turns). This way the forest chop wouldn't go to the axe. I whipped when there were 2 hammers left on the axe. Pyr in 21.
Chop comes in - Pyr in 16
Reset capital to build 2nd axe
Worker moves to river grass 2e, sets to cottage (again to avoid sending the chop to the second axe), also MM the capital to avoid growth into unhappiness.
Whip second Axe with 4? hammers to go, MM into starvation to maximize hammers (10 hammers per turn at size 2)
As soon as 1st whip happiness drops I let the city grow.
Chop comes in:
Pyramids in 20 turns
I can see the value of the second method - and it may be able to be tweaked further. We wind up with a mine, a cottage, 2 axemen. Unfortunately we finish with some unhappiness which caps our size at 3. But the biggest drawback is we don't get the Pyramids until 3 turns later than the first version.
A possible blend of the two could give us a single axeman and the Pyramids in the time frame of the first, but I'll have to do some more testing. In the mean time I have to do some work here
