But you say you just build enough military to defend your cities? I generally play on small/standard pangea or continents and if I don't build a decent military force early on, I almost always get attacked. And it's always nasty... That's why if I go for con/dom VC I always research the techs needed to get my early UU and take out my two closest rivals before 900BC. That way I'll have lots of land and can foucus on settlers, culture and more military.
How many cities do you have around 1000 BC when fighting before 900 BC? I'm opening up a few of my games around 1000 BC: 10 cities / pop 29, 6 cities / pop 15 (poor food, close neighbors), 12 cities / pop 20, 8 cities / pop 24, 10 cities / pop 24, 6 cities / pop 24 (with 3 catapults...don't remember what I was doing in that game...must have been attacked early). I try to expand as fast as I can during the land grab phase and then start developing/growing from the core outward.
Actually I don't have enough military to defend cities while I'm expanding, just to garrison them. If the AI attacked the warriors wouldn't hold up.
But as I'm expanding I try to find the right time to get the capitol and/or another shield-capable core city or two off of settler/worker production and on to barracks and real military. "The right time" has to do with how much more land I can settle and how much settler production I have. Usually I have 3-4 barracks cities pushing out spears and some offense around 1000 BC but am still expanding with the other cities.
I also have the road network established for defense and tiles improved for the growing population to work, so I can usually make military at a decent pace once the barracks are built.
I don't mind so much that it triggers a GA because if I don't take theese two out, I'll have problems later on. Especially if they got horses and I don't.
I usually expand quickly enough to get either iron or a horse, but even if I don't I manage to produce military quickly enough to overpower a single AI civ. I guess my goal is to grow to outproduce my enemies and then crush them.
I'll try swapping the citizens tiles, I've never done that just the scientist/taxman/entertainer swap.
The Emperor AI only has to collect 80% the shields and food we do to build and grow. But it is stupid when it comes to allocating its resources and has a lot of food & production overrun. 4 or 5 spt is low-waste for anything over 10s. 6spt wastes a fair number of shields except on 30s or 60s builds, so a town making 6spt is a good candidate for micromanaging up or down. 7spt is good for 20s builds but wasteful for 30s builds. 8spt is ok for 30s or 70s builds, great for 40s/80s, wasteful for others. 9spt is wasteful for just about everything, MM that city! 4, 5, 7 and 10 spt are often where I want to be in the AA. 14 spt is good for 3-turn 40s units if you can manage it early.
But of course don't alter production for nothing. There should be an advantage achieved. I'll sacrifice growth speed or even take a few turns of food shortage to reach 10spt for military builds. But usually I'm finding more growth or more commerce when reducing an inefficient number of shields to a more efficient number.
Of course if one is really anal or really needs all the help he can get to survive you can MM several times over the course of the build. That's not fun for me, so I usually avoid that except for settler pumps that don't work right without MM, and sometimes in the very early game I'll sometimes MM per-turn to maximize a food bonus by sharing it between towns. But usually I aim for an efficient number of shields.
Edit: If you're a beginning micromanager you may not have noticed that the F1 screen can be sorted by shield, food, commerce and other production. When I MM I usually sort F1 for shields and look for the inefficient numbers. I sort by commerce a lot, too. Sometimes it's surprising which cities produce the most commerce.