After reading the Food article again, I can see a bunch of mistakes & might try starting the same game over again.
After viewing that save, I think that save especially relevant. With respect to your capital, it looks like you didn't focus on developing it into a 4 turn settler production city/settler pump/settler factory. With two bonus grasslands and a deer, such a city can make 5 shields per turn at size 3 with both bonus grasslands mined, and the deer irrigated (after it got chopped). With two more two food tiles that also produce a shield, that makes for 7 shields per turn at size 5. With freshwater like your capital's lake, such a city can produce a settler just in time as it grows to size 7 (or a bit smaller, which works out better for getting more cities up quickly and thus more overall growth eventually).
What I think you did: Your initial worker did a little capital development and then went off to road or help another city.
A better plan: Your initial worker stays around and develops the capital until it can produce a settler every 4 turns, or in some situations produces 10 shields per turn and can produce a warrior in one turn, then a settler in 3 turns (or later after barracks, maybe a horsemen, then 3 workers, then a settler). But stick with trying to get a settler out every 4 turns.
When cities get built earlier and one's empire has enough workers to develop core cities and maybe even grow cities, then keeping in technology on Emperor becomes more feasible.
Also, you have a large number of medieval infantry at your capital. If they and your other units were out trying to attack, you might capture some cities and have a better economic situation.
