I'd never won a Monarch-level game until I tried a variant of this strategy. I'm just not ... dominating ... enough, I guess. I actually have never managed to win at Prince level by domination, either.
So here goes ... I won two out of three playing the same general strategy. In the third game, I was doing fine until Hattie/Egypt, allegedly pleased with me, attacked in 1926 with way more than I could deal with.
The other two games I won in the 1960s. I'm sure I could get it to be earlier if I specialized better, but the following conditions/circumstances worked for me:
1) I played as Gandhi. No particular reason, but I did go for early religions, costing myself growth. My goal was to establish six cities, three of them good ones, without attacking the AI. I quit early on a couple of tries where I was hemmed in too quickly. In one game I built my six; in the other win, I built four and took two barb cities.
2) I managed to build the Parthenon, Pyramids and the Great Library in both wins ... once in three separate cities, the other time Pyramid/GL in the capitol.
3) I founded two early religions in both games and a later one in both games; ended up with five in one game and six in the other. I built very little military. I changed religions whenever my more powerful neighbor(s) did and gave them anything and everything short of declaring war.
4) Was able to stay relatively even on tech through liberalism, in the 1500s, which is when I started moving the culture slider to 60/70 percent ... later to 80/90.
5) I didn't get nearly as many great artists as one clearly can by specializing, but it was enough. By the end I was at about 500/420/380 for my three main cities.
Posting just because ... that I could do it shows that you can win this way with a big margin of error, really. Because I did very little micromanaging after getting the cities up and running. Games took less than three hours.
(Update): By playing better and micromanaging better, I was able to get wins in the 1800s. It doesn't seem that any Wonders are necessary, though if you can get any of the early ones it surely helps; and I got Great Library every time, which let me keep up with tech as long as I wanted.
The hardest part for me was to get six cities and three religions going, early. The "easy" way is if you have room AND the game lets you found three early religions ... just stay friendly and play it out. It happens.

But my favorite win ... I only had four cities and two religions for a lot of the game ... but finally started overwhelming my neighbors with culture around 1400 and picked up three-four more cities and two more religions that way. There was plenty of time left for building religious buildings.
