Help with power democracy

I've gotten back into this game recently and have been trying different ways of achieving a strong PD, but I always feel as though the description of how much I should be dominating in a PD is far different from my realities.

Mine always start great, but but Industrialization all my cities routes are filled and my transports lay empty, relationships with the AI start to falter, and I'm never usually more than a few techs ahead of the AI. I've attached my save file and it would be much appreciated for some tips on how to proceed from where I am now. MGE edition with one of those AI patches found on the forum.

A brief summary:
Russians were wiped out by the Persians early on
Persians built Magellans, which I captured after I realized I had no chance to build it before them. I have Leo and Mikes, and have Theology but haven't started on JSB

Have a look at this succession game thread.

I think your biggest problem at the moment is that you don't have enough cities. If you prefer to play with a relatively small number of cities, that's fine, but you will have to invest in Hanging Gardens/Cure for Cancer or a bunch of courthouses. This Succession game was restricted to one continent.

At the moment, the first citizen in your cities is unhappy. Since each city uses a maximum of 2 luxuries per citizen, cities can only celebrate when there is an even number of citizens, so you are losing out on WLTPD growth. Adding cities creates additional base unhappiness in your cities, but after a while, the first citizen starts to be "double unhappy" or a "black hat." "Black hats" only need 2 luxuries to be boosted directly to happy status, so, if you are using luxuries anyway, they actually make the civ easier to keep happy.

Related to the above, why are you running a 70% luxury rate? 30% keeps order if you move an Avaris worker to ocean. Related to that, you have citizens working grassland without roads. Your engineers should be making roads for those citizens. Roads for worked (or soon to be worked) grassland/plains should always come before irrigation. With WLTPD/WLTCD, a democracy/republic only needs one food surplus. A city on a grassland can support a settler and use all the ocean and grassland tiles in its vicinity without needing any irrigation. In fact, if you are going to irrigate, it may be a sign that you should be building a new city instead.

The Prof's advice is always valuable but the best way to sharpen your skills is to join the ongoing GOTMs and see how others play the same game. GOTM 165 was just posted a few days ago. Start playing, post your progress in the spoiler thread, and see how others are doing at the same epochs as yours. Take a look at past spoilers to get an idea of how things are typically done.

Prof. Garfield, thank you for the response.

Just to clarify a few things: Yes luxuries were high, but how are you supposed to WLTK without high luxuries? Is that where the black hats come in? About how many cities do you need until black hats start showing up?

In regards to building a new city instead of irrigating, are you advocating building my cities closer together? I've never been one for ICS-style gameplay although I guess it might be necessary for this strategy.

Finally, when should I be irrigating?

On a large map, 15 or fewer cities guarantees that all cities in a democracy will have the first citizen content. 45 or more cities guarantees that all cities will have at least one black hat citizen. Between that, you will need courthouses or HG/CFC to celebrate consistently. You are running high luxuries, but very few of your cities are celebrating, so you are wasting arrows that could go into taxes or science.

I don't normally play ICS. I am suggesting that you transport your settlers/engineers by road or boat to unsettled land. New cities give new caravan commodities, which means more income. I suspect that the "correct" time to irrigate is when you run out of land to build new cities, but the point of civ is to have fun, so you may decide at some point that you have enough cities and start irrigating once you've finished your roads (and railroads). There may be times when it makes sense to irrigate a square or two (or those around your SSC), but you should always ask yourself what else the settler could be doing and if the extra food is really worth it. An engineer can make as many as 3 roads in the time it takes to irrigate a square; if all those squares can be worked, that's 6 arrows for 1 food.

Also, see this thread. In particular, posts 4 and 20. (most of the thread deals with a technical question that is of little value in gameplay but was open for a long time)

I don't play under democracy, but if I'm running a food surplus in the early game I'll often start pulling off workers from their tiles and making scientists. Getting those corruption-free beakers can be a big deal in terms of making your library-builds effective, especially if you don't have trade routes set up yet.