@ Burrito_X & MasterDinadan
How more population means more gold? It's pretty simple, and has very little to do with specialists: more population equals more workable tiles. Those farms will net you more citizens to work over other production&wealth tiles, such as mines and water. More wealth tiles worked (such as coasts) is pretty straightforward, but more production aswell means faster building of wealth increasing structures (markets etc), which, in turn, will net a big income increase much earlier than the AI.
The AI shortcoming in this department is, as far as I can see, that it somewhat takes into account the new balance, yes, but doesn't consider this exponential gain at all. It just choses the improvement that best fulfills its IMMEDIATE need. AKA, if it needs money, it will build the trading post that will net it those couple gold coins per turn right now, not the farm that would represent 10 times the gold gain thanks to this domino effect, but in 100 turns.
The issue with happiness isn't an issue at all: if you are expanding, actually mostly ignoring happiness is one of the easiest ways to rushwin the game through conquest even in vanilla. The faster rate at which your population increase, and as such your production, makes it even easier since you'll crunch out settlers first and military units then much faster, to grab those new luxuries that will keep happiness still somewhat under control (not to mention how it's already the best idea to just RAZE & RESETTLE the conquered cities in vanilla, with boosted farms it gets 10 times better).
For more conservative games, such as when you want a culture win, it's still pretty easy to keep happiness under control even with higher population: you have more gold and production; with those you can buy - or build - happiness wonders and buildings faster, you can buy tiles towards that luxury faster, or even just buy it from an AI civilization.
As you pointed out, even in vanilla at mid difficulty levels you tend to gain a huge advantage over the AI since the middle ages: it's for these very same reasons (not a coincidence that the gap becomes so evident right after the first techs which boost farms and production). By making food and production tiles more valuable in the long run, the issue gets worse since the AI isn't capable of planning ahead taking "the long run" into account. As long as you can keep 'em at bay in the first stages of the game (not difficult thanks to the 1 unit per tile mechanic and the suicidal behaviour the AI loves to keep), that's it, you've won. There's not even any real reason to expand once you have some cities and some chokepoints to control: you can just defend for a while, and then conquer everything without any effort a bit later when you'll be an era ahead of everyone else.
Right now I'm back after a game played this time with a setup similar to yours, Burrito_X: Valkyronn's Economy mod, the freshwater farm balance mod, the Great Persons balance mod (that one is just perfect, it makes 'em useful while they still are too rare to really affect too heavily the wide balance), and a single small modification by me that just gives +1 to mines after Dynamite, so that they can compete with lumbermills. Main difference is, this time I left out both the modded buildings and wonders.
The issue is still there, not as big, but still there.
I guess I'll try a different approach: leave the improvements as they are, and boost only the resources. Wheat, animals, strategic resources etc. At least on those the AI will always build the right improvement as I would do. Only obvious shortcoming of that approach is, though, that luck becomes much more important and starting points would become more of a win or lose scenario: you get the wheat, you've won, you don't, you're in for a world of hurt >_<
P.S. BTW, MasterDinadan, if you can tell me where I would have said that "the mod is broken" I would be sincerely grateful. I love science fiction.