Concerning the empire becoming too large, you have to adapt yourself to the situation. Here's an example from a game I played:
In 220 BC I had 27 towns. I was playing on a huge continent, with 18 empires, on the longest time rate.
My continent was huge, the biggest of all three and I'd attacked and conquered all 5 civilizations that were on my continent. I had 5-6 cities on my own, with 21 puppets.
You can't know how large this is without seeing it. As I'd captured lots of workers, I built lots of roads: when you have 20 workers and your Roman legion building roads, this is fast and your cities become much easier to defend. Since I knew I was now alone now on this devastated continent, I didn't need much defense. I could just work on my town.
It's worth mentioning that the game's happiness balance is a bit wonky, which is probably the cause of your "insane lack of happiness". Puppet cities don't produce much unhappiness: it's the people in your other cities that are the cause. For example, in my case, I had lots of gold tiles and all the possible luxury resources besides three(whale, pearls and ivory).
I had 5 cotton tiles and 3 silver tiles, but they don't contribute any happiness after the first tile. It would be nice if they at least provided something.
With all six of my cities, I bought or made a Colosseum and a circus if I was able to.
Actually, I'm now at 1720 AD in the timeline and the only thing I did so far is work on happiness. I'm at 40+ town's (I made a new one to cover all land space) but the basic problem is that as soon as I got few happiness points, the town grew up another tier and I went back to negative. All my research and social branches are concentrating on happiness.
When I got the +20% happiness bonus, I had a huge jump from -3 to +12.
Then when I made the Forbidden Palace, I went to +30 or so. This is when I started to annex all my puppets. Now that these cities are no longer puppets, they are mine and I'm producing buildings all across the continent. This is hard to keep up: one turn my income is +60 gold, the next it's -20 (this is an exaggeration, but you get the idea), but overall this is worth it. This is especially true during a Golden Age, where I go to +350 gold per turn.
Also, as a result of having all the maritime neutral allies, my food bonus is awesome, meaning my town grew up pretty fast. I see the other empire's best town has nine people; for me, nine is the average of all my towns, including my latest.
My army is still composed of legions and cavalry. I haven't ever needed to create a new one since the last two empires are far away and I only need to kill barbarians moving around. As for tech, I'm about to discover Tanks! In the year 1750, I'll be producing tanks, and I don't think their little gunmen will be of any match.
So overall, it depends on your surroundings. Can you balance lots of towns over short periods of time? If so, you're going to be pretty powerful. I'm about to reach 1500 points. I don't know how good that is, but if I look at the best computer with his 25 towns, he doesn't even have half of this.