I will teach you a strategy that I like to use on Immortal with great success!
Check this out:
I started cottaging over your many, many farms that weren't feeding specialists, especially the floodplains. I also moved units around ASAP for happiness, especially fast-moving chariots, from low-pop cities to high-pop cities. That allowed me to work the cottage tiles right away. I had to cancel all your random roads; there are already way too many of them. Your capital is amazing for farming great people. Actually amazing. There are soooo many food tiles. I built libraries with the help of organized religion and slavery in nearly all of your cities. I put 2 scientists on to get your first great person. I started a golden age with them, and flipped into caste system and pacifism. If you had access to representation, I would have flipped into that as well. Note: there is NO ANARCHY during a golden age, so you can flip into civics and out of civics without worry. You also have a PHILOSOPHICAL LEADER, which makes this strategy extra-effective as they have a 100% bonus to generating great people.
NOTE CAREFULLY! You can have unlimited scientists, artists, and merchants in a golden age, so make sure to STARVE your empire! Why? Because the beakers you get from great scientists/merchants are WAY MORE VALUABLE on-net when you bulb key techs with them rather than the few bonus tile yields you get from working tiles with citizens instead. If you weren't so late in tech, you could beat the AI to Liberalism and other techs that get you free things for being first to research them (techs, great people, etc). This allows you to leapfrog the AI easily, even on Immortal/Deity.
You will also see a picture of all the cities I am starving. I am running scientists to the extent you can't see them listed in total. You can also see all of the cottages and happiness differences that have turned your economy around.
As the cities were about to lose population, I checked how close they were to starving down to see how many turns until I got another great person. It's a judgement call if you want to try starving to the point of losing pop if you're close, but I generally never do that unless I'm guaranteed to get a great person. You don't want to starve to nothing or cripple your economy for when you flip out of the golden age. During the last turn of the golden age, I swapped back into slavery and organized religion so I can build more buildings easier and go back to working the cottages. I was able to catch you up substantially with the AI in tech by bulbing with great scientists and creating an academy in your highest-yield research/commerce city. The final great person I got was a spy (yuck), but they'll be perfect for setting up the next golden age. Berlin is already getting close to generating another great person. I also turned off the slider to make use of your markets. Having the slider at zero when out of a golden age is a good idea with a lot of financial buildings + cottages because you will get an income bonus. Research the next tech once you have enough money to do it all at once. Doing this also avoids the rounding losses that CIV IV calculates when adjusting for your actual income rate. This is more important with a smaller empire earlier on than later in the game, but it still makes a difference if you have a lot of cities because each city will have its own slight loss due to rounding. I also built more windmills because they're going to feed your cities better than unworked mines while still allowing your to build wealth. After swapping civics, I re-balanced the empire to work cottages again, dropped the research to zero, and ended the golden age.
tiles again). 
