OK checked out the save and there are a few things that would help.
- You have too many specialists.
They're good, but not at the expense of everything else. It's fine to have one city with all farms and a bunch of specialists, acting as a great person farm, but using them in all of your cities means you have very little production and commerce.
Your cities can all grow larger. This is the most glaring issue, and you need to let them grow. You haven't built granaries, and your specialists have stunted their growth. It's a good idea to allow your cities to grow at least close to thier max happiness levels, if not max it out. Ditch the specialists and grow them. Once it hits the max, you can lock the growth, then reassign specialists or just work more tiles (e.g. more towns).
- I'd take down America. More land and resource is always a good way to increase your power and score, and it's so lightly defended, so why not have it as your own?
- Your cities are not focused. Kufah, for example, is building a bank, yet it is barely pulling in any commerce! I'm going to use the world builder and reorganize your cities the way I would use them, then attach a re-save for you to compare. I'll detail my changes one by one, explaining why.
Mecca (Commerce)
You were already running Bureaucracy, which would be far more effective if your capital were more focused on commerce. Work cottages here into towns, and don't worry about production unless a new building becomes available. Forget about wonders etc. and just bring in the commerce with your bureaucracy. With the way I set it up, you can either get 216 beakers by emphasizing commerce, or 3 turn grenadiers with 170 beakers. At this point, I'd probably be pumping out the grenadiers for taking over America, but otherwise I'd be working those towns.
1. Changed most tiles to towns, especially the rivers (+1 commerce). Check out what it would look like if you had been developing cottages for most of the game!
2. Ditched the specialists.
3. Irrigated the two grasslands tiles to the southwest, for three reasons. First, you can use those tiles when you want to grow your city. Secondly, if you want to build a new building, you can use the farms + mines for more production. Lastly, Medina needs the irrigation path.
4. You didn't need the forests. At this stage in the game, you should be trading for more health resources or conquering land and taking them for your own. I turned them into farms and cottages.
Medina (Commerce)
Since it's a coastal city, with several coastal tiles, you may was well go with a commerce focus here.
1. Irrigated a couple of tiles from the river at Mecca. This allows you to work both of your production tiles, work cottages on the rest of them, and still grow.
2. Again, no specialists. You need this city to grow.
3, This city desperately needed a Granary, before the Observatory. It's short on health and also needs to grow. It should also get a harbor, which is relatively cheap to build, before most other buildings. A harbor will give you more health, as well as extra commerce from your trade routes.
Najran (Military)
Plenty of hills for high-production mines, so I declare this town to be one of your military production houses. It really needs growth. Right now you can build grenadiers there every 4 turns while still growing slowly, but I'd probably emphasize growth and let it grow to size 17. At that size, you'd be at your current health maximum, yet you'd also be able to work every tile available and produce a grenadier in 3 turns (actually 2 every 5 turns, with the carryover).
1. Stole the shared tiles from Baghdad, it wont need them.
2. Windmill was changed to mine. You don't need any commerce here.
3. Added Watermills along the river.
4. Deleted your libraries, etc. just to show that you don't need them here. This is a production house, not a commerce center. You get to keep the market and grocer, because they can they give you happiness and health, respectively.
5. Replaced those commerce buildings with a Forge and Granary.
Kufah (Military)
Same concept as Najran. You don't need the bank here that you're building. Just build military and grab more cities! I think you'll have enough food to work all of the tiles after it grows, but I didn't verify.
What you'd want to do is, if you have too much food, change a farm to a watermill or workshop. Not enough food and you can change a mine to a windmill. It's good to have plenty of farms while you're growing, however, so that you can grow more quickly (and put in those granaries!)
After your units get some experience while taking over America, you'd be able to build the Heroic Epic here and really pump out those military units.
1. Changed Windmills to mines.
2. Changed cottage to farm.
3. Again, I deleted the library and observatory, and replaced them with a forge and granary.
Bagdhad (Great People Factory)
Finally, a city I'm going to let you keep your specialists in.

The only thing you absolutely need here is a granary. This city should grow to work all the farm, and then you can max out those specialists. Did not change anything here. You can just farm everything, and build globe theater to eliminate happiness issues.
One thing you might consider is switching from slavery to caste system, so you can have unlimited artists, merchants and scientists. On the other hand, with slavery and the globe theater here, you can whip out some military units or some buildings. Firstly, you need to whip a granary, which will allow it to grow back more quickly.
Chicago
No comment, really. Not sure why you took it? Unless you were having border contentions over that deer, there's nothing there that I would want.
Damascus (Commerce)
Similar to Medina. It needed some more food, so it could work the Incense.
1. Changed mines to Windmills. I left it stagnated right now to show you that it has just exactly enough food to work every relevant tile. I'd first favor the sea tiles over the 1 food tiles, however, in order to let the city grow more. Once it hits the max it'll be balanced to work every tile.
In conclusion, this is only what I would have done with this empire. Others would surely do things differently, but identifying what your city locations are best suited for, and specializing your cities to take advantage of it, are important for everyone.
With this new save, not only are you currently generating more beakers, despite the fact that I deleted a couple of your libraries and observatories, but you also now have two
dedicated military cities that can pump out units for the rest of the game. Of course, I cheated you some towns at your capital as well, but let's just assume that you planned it that way from the beginning, shall we?

Once you allow your cities to grow, the differences will be even more dramatic.
And I would smash America for sure.
