Going to a 100% cash economy is a perfectly good strategy; I do it rather often. (I'm also an Emperor-level player, roughly, but I've also won deity a few times.) There are a few things it sounds like you could do to make it more effective, though. Be warned I've never played C3C: I'm slowly picking up the differences, but may make a few mistakes in the meantime. Hopefully someone will come along after me and point out where I went wrong, if necessary.
I really don't know what tactics you're currently using, other than what you mentioned in your post, so forgive me if any of this is redundant or obvious to you already.
1) You mention "improved military support" for cities above size 6. Are you playing as a Monarchy? If you're playing builder style, Republic is infinitely superior. You get one extra commerce arrow for every worked tile in your empire that already produces commerce, and less corruption to boot. Your ability to stay current in research after the middle ages will greatly increase if you switch to one of the representative governments. If you *are* already playing as a Republic or Democracy, then you have no unit support -- increasing the size of your cities won't help in that regard.
2) Be selective in what you build (purchase). This probably goes without saying, but it's worth mentioning. If you have all 8 luxuries and a marketplace in a size-12 city, you do *not* need a cathedral, too. You can save a surprising amount of money this way. In fully corrupt areas, purchase as little as possible. Temple or library to expand borders only if necessary (you can even sell it again afterwards), marketplace for happiness, possibly aqueduct for population if you have the cash and happiness is not an issue. That's it. Irrigate everything and turn your excess citizenry into taxmen or scientists, whichever suits the situation. Make the city produce wealth. If you want to work the unused tiles, make more cities -- 2gpt for a hospital is too much to spend for a fully-corrupt city. If you have good territory, this tactic can net you easily 3 or 4 gpt or beakers per turn, per city.
3) Consider using your core's production strength instead of (or in addition to) cash to rush your builds. This won't always be appropriate or possible, but if you reach a position in the game where you have nothing necessary to build in your core cities, build military units instead of switching to wealth. The military units can be shuttled over to your developing cities and disbanded for a portion of their shields. This will allow you to retain your income for things like tech-buying. Five high-production cities with factory and power plant can turn out 20-25 cavalry in ten turns; these can in turn be disbanded for 20 shields apiece, which amounts to 400 or 500 shields total, enough for 4 or 5 harbor/marketplace type improvements. Switching those five cities to wealth for the same ten turns gets you only about the same amount of gold as shield-rushing would get you shields (pre-economics it gets you even less), enough to cash-rush only 1-2 improvements. In general, you come out way ahead using your production capacity.
4) Another thing you may know, but worth mentioning anyway: when behind in tech and trading for it: trade smart. Never, unless in dire need of it, buy a tech when only one civ knows it. You'll pay twice as much. Wait for two or more to have learned it. And even then, keep a sharp eye out for 2-fers, 3-fers and more-fers.
5) Don't forget about espionage. Starting sometime in the industrial ages, it starts to become cheaper to steal tech than to buy it. Take advantage of this -- get the necessary tech and crank up the old espionage machine. Worried about war? Don't be -- you're playing on archipelago and by this time should have a basic rail net and a couple of stacks of artillery, plenty to defend against the motley assortment of units the AI will throw at you once you've distracted them with two or three military alliances against them. (One more note on this: as far as I know, the cost/benefit analysis on 'steal safely' versus its opposite comes down on the side of the cheapest option. I'm not sure, though -- maybe someone could clarify.)
6) You can trade your resources, even if you have only one source. (You simply won't be able to use it yourself for 20 turns.) If you haven't done it before, you'd be amazed how much mileage you can get out of a single source of iron, for example. Even at deity you can get an entire middle ages tech just for one little piddling iron resource.
7) Whereever and whenever possible, request gpt in return for your trades instead of straight cash. In the long run, this will tend to bankrupt the AI, since they don't know how to budget properly. In the long run trading for gpt has an effect similar to starting lots of wars -- it will slow down AI research and decrease their cash flow.
8) And finally, the thing you didn't want anyone to say, warfare. You don't have to go all out for conquest to get a great benefit from it. A strike against a single civ, timed right (cavs vs. muskets or tanks vs. infantry are the best options), can give huge dividends. Not only do you gain the extra territory to power your victory, but you're also likely to be able to severely hamper the AIs in a way that you've probably been unable to take advantage of much in the past. Why? You're playing archipelago mostly -- that means far fewer wars than on other map types. The more the AI war -- as long as it isn't against you (and sometimes even when it is) -- the better off you are. When the AIs are at war, research slows down -- AIs have no concept of how to manage happiness in wartime as republic or democracy and usually wind up driven into less efficient governments. Trade routes are broken, so luxes are lost (and may become available to you). Trading of the techs they do learn gets severely disrupted. Empty spaces may open up in former enemy territory in which you can place a well-timed settler to secure a key resource. I played a deity-level SG once on a Pangaea where the AIs all unaccountably avoided war until into the industrial era, IIRC. The tech pace was unreal; although we were keeping in touch tech-wise, it was taking us practically everything we had to do so (selling our only iron while our cities were defended by warriors and horsemen in the late middle ages, for example). We got to railroads just as we were finally getting something more than cardboard cutouts for a military, only to find we lacked coal. Still underpowered, we organized a quick strike against one of our neighbors to claim it, and suceeded despite also having to fight off a half-hearted opportunistic war against us from the other side of our territory. That opened the floodgates; from then on out it was constant war, most of which we stayed out of, and the tech pace dropped to a crawl. We won by conquest, by our choice, but any victory condition would have been possible.
Consider phony wars, if you really don't want to fight: declare war on a distant rival, sign a few military alliances, and just play defense on your own island while the AIs duke it out.
I can't believe I wrote so much.
Renata