I've only recently moved up to Noble, but I have a similar issue to you - I hate using Slavery, and only use it if absolutely necessary. I still have it running, though - it's better to have it and not need it than need it and not have it. And it can be -very- handy for getting rid of unhappiness quickly, if necessary - and I have less of a conscience issue whipping away dissenters
Anyway, if you have science at 100%, you're not broke. Drop it to raise gold, if needed. In fact, if you're running science at 100%, especially in the early game, you should be expanding more -anyway-. If your science is higher than 60% (some say 30%, but I like teching decently), you have room to expand more.
Don't try to make every leader happy. Pick one or two, who'll be useful or easy to manipulate (sadly it's all too often one or the other...), and do everything you can to make them happy. Ignore the others. In my most recent game I focused on making Joao and Lincoln pleased - I'm now in a Permanent Alliance with Lincoln, and we have Joao as a voluntary vassal, which means despite my having half the military of Justinian, the main military leader, he's too nervous to even -touch- me for fear of the dogpile mayhem he'd be inviting.
GP farms are incredible, but I often end up with them by accident - my most recent game I managed to build two on purpose, one a National Park site that was left in the heart of my empire, the other a Korean capital that had more food than I knew what to do with. You -will- want GP farms, they can improve things far beyond what you'd think.
As for military, I find it best to assume I'm going to invade -somebody- sooner or later, and have at least one stack of doom ready in my territory. Since I've had a lot of sea maps lately, I define an appropriate stack of doom as one that requires no less than ten Galleons - along with city defenders in each city, and the ships themselves, plus escorts, this is usually enough to deter attacks.
As for that massive tech lead, harness it. You have rifles while they have muskets? Invade a couple people, soon you'll have Modern Armour while they have rifles. Better yet, find someone else who's a fast techer, and trade. I've used this to recover parity after mistakes several times - one well-traded tech can net five or six extras in return, a pretty good investment.
I used to be a big builder-type, trying to avoid war unless I had an absolutely crushing advantage, and even then shunning it if possible. I found a good rule of thumb to break that is thus: Try to start a war within the first thirty turns, and end it within the next ten. If you can capture another capital site early, you'll be -amazed- how much of a surge your empire'll get.
Remember, Civ is a game about force-multipliers. Every bonus you get early on gets better the longer you hold onto it, while every disadvantage you suffer gets worse the longer it takes you to get rid of it. Two capitals to everybody else's one is a -huge- force multiplier early on, and after feeling how much of a boost that gives you, I guarantee you'll want to be capturing three, then four, then five...
This game is all about playing to your strengths: your strengths on the map, your leader's strengths, your civ's strengths... Shaka is an aggressive little Zulu with an early unique unit (and a unique building that only helps in conquest). So leverage that! Get Impis out and about as soon as you can, and watch them hamba kakuhle all over your opponents! 
