My advise for this session is:
splunge the 2nd:
First of all, Entremont at size 2 is way too small for this stage of the game. When producing workers, you should be running at 5-6, or when producing settlers at 4-6. Entremont could net you twice as much commerce (and shields) as it is currently making.
As a consequence of this, you need all those scientists in order to finish Philosophy in 2 turns. With Entremont at let's say size 5, you could probably finish Philo in 2 without having to burn so much food.
I also notice that Verulamium is not founded on a river, while it easily could have. 1W or 1NW would have been a much better site. This wastes food during despotism, and you'll need an aqueduct later in the game.
On the plus side, your naval exploration is off to a good start, and you can probably count on the slingshot (unless you suffer the same fate as templar and loosing the race one turn before the finish line...)
creamcheese:
Not much to be said here. Slingshot achieved, naval exploration started, decent expansion. You definitely have the game under control now.
I think there is one point for improvement: you have many workers improving the tiles between Lugdunum and Camulodunum,
while the two floodplains are still unimproved! These floodplains are among your most powerful tiles (besides the deer and the cow). It should have been a high priority to get them irrigated already a while ago. (Paperbeetle, templar and myself are already using these tiles for a two-turn worker pump by now, which will help with getting the core improved quickly as well as building war roads towards our neighbors pretty soon.)
Lots has already been said about the GLib... I also think that a wonder in this type of game at this point of time is a waste of shields. (Even the Zeus Statue is not worth it in my opinion. Better build 10 horsemen instead...) But in any case, playing two versions of the game for comparison is an excellent idea. If you have the time, go for it, it should be quite instructive for all of us.
In your game the AI is strikingly backwards?! (Especially Rome.) This may make the game a bit difficult for you:
a) they will build lots of units, if they don't have libraries, markets or wonders to build...
b) they can't do any useful research for you...
Perhaps you should gift them up a bit.