If you are willing to chop it, you can build them without stone or industrious even on emporer.
Beeline monotheism, found and adopt jew, organized religion, chop.
Unless you run caste and assign alot of specialists (and are philo?) this is likely a fatal strat.
Using the chop+whip overflow for cash exploit and US, a new level of cheater domination may be possible.
What does Caste System have to do with rushing the Pyramids???
Caste System ONLY allows unlimited Artist, Merchants and Scientist NOT Priest or Engineers.
This Civic would be way overpowered with it allowed you unlimied Engineers, you'll just beeline to COLs and Philosophy Slingshot and just Assign Engineers and receiving unlimited GEs, Rushing Wonders like mad :S lol
but this would be at the sacrifice of Slavery, Would work every well with Gandhi (Spi/Phil) though.
Pyramids, NEVER build them unless it's part of your strategy, to be honest there is no best time to build them on higher levels. Just pray that you'll get there first.
the bright side of not completing the Mids is you get ALOT of cash as compensation for 100% research for a LONG LONG Time so losing them isn't necessarily a bad thing.
but if you must get those Mids there are a couple of gambits you can attempt.
Philo - Oracle/MC/Forge gambit
Ind - Stone/Manonry/BW/Chop.
If you have neither of these, Pray for the RNG gods to be nice to you.
I have gotten the Mids on many occasions after the discovery of Mathamatics for 30 base Hammers Powerchops. Especially with Ind and Stone, that's 75H per chop. Very nice.