As far as Rome, have you tried going a couple food techs like agriculture, AH, wheel->pottery maybe, then going IW and starting your rush? Going priesthood and masonry may be slowing it down significantly. In my opinion, which is not backed up by anything other than personal experience playing the game, the ideal preat rush happens with about 3-4 cities, and you get a stack of 8 preats attacking a neighbor AI who has 3-5 cities with archers in them. Take him out, those cities start whipping praets and you go on to the next civ. You can usually get 3 civs in your empire and have 12-15 cities before the AI gets longbows.
I still think even with caesar rush > rex and you need to prioritize the techs.
No offense, but are you talking of Deity? I got IW by Techtrade at 2000 BC, I dought that I could have been that much faster if self-teching it, and skipping on Oracle imho is just not possible in a competitive approach. CoL allowed me to get Alpha, Math, Currency, Calendar and Construction while I researched Aesthetics Literature Music to have further Tradegood. I cannot imagine how I should keep up in tech without it, and IW 2000 BC is still very early imho.
The problem was imho building the Mids by myself, it's just a loss of Hammers one cannot compensate for, and, the start was really really crappy this time, no Gold, just a Stone Hill, some Corn and a plains Cow. Map wasn't better either. If I had not built the Mids, I could have built 4 additional Settlers, which would have given me a total of 9 cities, that's a base to start from on Huge imho. Whip once or twice in every city, and you got your Stack with which you can go rampage. 5 cities were too few, I don't think building Granaries was a fault, neither Oracle, simple rex would have given me a much stronger position.
It's just hard for me to adapt from Incans, where one can build all the wonders one wants to Romans, where one has to conquer them. One must note though, that I would have won this game even with as little as 5 cities, I can post the save if someone is interessted in it, I got 10 cities at 600 BC and a Stack of 20+ Praets and half as much Cats + Trebs on the way.
I'll get myself a "real" start now. Now that I learned that one has to play with temperate climate (to have enough forrests) and that one has to build Settlers / Praets and simply conquer the world instead of building it onesself, it should be easy, I'll post some progress later.
Since we're discussing rushes, this is why people love Gilgamesh so much. Just imagine being able to start your rush with bronze working only. 6 str axes against archers are really good. The courthouses at priesthood are icing on the cake, since now you don't really need to oracle as badly. Also zigurats cost 90 hammers vs 120 for a normal courthouse. Anyway it's just another leader to consider along with Egypt. Sumeria starts with wheel and agriculture so all you'd need to tech is mining -> bw and maybe pottery and you're ready to attack.
Thx for your explanation of why Giggles is considered to be a good leader. When I first saw him, I thought "ugh", because I could see anything special about him. I still find though that Axes suck in general, I can imagine that STR 6 ones are better and I can imagine how this specific rush works, but I don't wanna play him, he actually looks like a sheep-herder (or sheep-horder for those watching Southpark

) . Maybe I have to if I wanna get EQM someday, then I'll remember your words.
Cya, Sera