For the curious, I started a game on Emperor (one below Deity) with Random settings on a standard size map. I am German on a small continent with Romans. My land is mediocre, with a cow icon next to the capital, mountains to the sorth, and desert to the north, with precious little room for traditional cities.
What I do is shoe horn about twenty cities in a space and terrain that an AI player might put six to eight cities. This gives me enough production and support for military units to build my army of Horsemen. Getting the horse icon is nip and tuck as there is only one horse icon that I have any chance of claiming.
The Romans are a tough early opponent because of their Legionaires (unique swordsmen). It often takes three to eight Horsemen to take out a single Legionaire. Despite this, my massive army of Horsemen backed by five catapults makes short work of the Roman Legion.
I am still up the creek as far as tech goes, as other civs are building second age wonders and I am still in the first age. However, slave camps would be LESS effective on my current map at Emperor difficulty with little grassland and only one cow and no wheat.
Still, I am out of the first age in decent shape with about thirty cities on Emperor difficulty, and no enemies near me. Unfortunately, almost half of those cities are destined for pop 2 or 3 because of the incredible build density. Still this is accomplished without cracking the whip in my own cities, and a mediocre patch of land. I did use the whip on captured cities, but even that is not a necessity, just a convenience.
So for those who find slave camps and whipping citizens to death distasteful, there is hope, there is another way. Try it, and get the message out.