You might try some tests:
Have your friend ALWAYS go for Pyramids while you go for something else.
Chariot rush to take the Pyramids?
Axe rush to at least THREATEN to take the Pyramids?
Spies to steal techs? (VERY powerful! LET him do all the research, spy points are cheap!)
A couple extra cities in high-food places with Cottages galore? (whipping, extra commerce)
Other wonders? (Great Library?)
Better civics?
Then after you've tried a few different strategies, switch sides, and YOU always build the 'mids and HE tries to overcome it. If the Pyramids are ALWAYS the deciding factor and can't be overcome because of your situation, then ban them. If they can be overcome, you've just found your rock-paper-scissors formula.
However, I'm thinking that maybe you guys don't know how to rapidly build up your economy/military and go kill someone. Most of these guys are shocked that the Pyramids aren't LOSING the game. This could only be if the non-'mid player isn't wisely investing the hammers he'd otherwise have available (or the gold he gets from failure).
But maybe the Pyramids are unassailable in your situation.
You've spent so much effort to make a "balanced game" that you didn't take out the one last unbalancing factor. In a normal game, there are other players to deal with, barbarians, goody huts, and so on that help even out the odds and keep the tech leaders roughly even. If you're both going for one wonder, the loser only gets some gold. With other players around, they're researching too, and can be traded with to keep your tech rate and income levels high.
Additionally, with other players and barbs around, if you are neglecting your military to, say, build an expensive Wonder, that could cost you.
There are tons of checks and balances in this game. Turning them off winds up making for weirder games.
One last idea you might try is the late-start game. Don't start in Ancient times, start perhaps in the Renaissance. Then Pyramids is irrelevant.
Good luck, and let us know how it goes!