@superslug, I do think I've cracked the Sid code to at least get a victory, and I think you can do it too. I may write it up, but it really just involves drilling every possible exploit as deep as it goes.
(1) Archipelago 80% water
(a) This limits the expansion power of Sid civs, which is a top advantage in addition to production discounts. They can only expand to the water's edge, and in a 60% archipelago, so they aren't oversized when you take them on.
(b) Many of the Sid civs will drown themselves in units and unit support costs when they can't expand anymore or war, eliminating them from being tech problems.
(c) If you are a seafaring civ, and choose all non-seafaring / non-commercial civs, you get a monopoly on Alphabet.
(d) You also get 3 move carraghs, and since AI don't "suicide" them to contact other ones, you might be able to tech trade as well since they won't be in contact for a while.
(e) You just need to be alone on your home island. If there is another civ, re-start.
(2) Pillage trade route.
(a) Free techs, enough said. Spend nothing on techs, build up a huge war chest (you will need it to rush Armies from a Military Academy for the conquest phase). Please do as
@Spoonwood says and re-acquire the lux every turn, in order to eliminate the chance that you could lose the pillage trade turn for turn. On archipelago - it's super easy to do this. Just forgo harbors in all but one or two towns you can cut a single road to. Leave 6 workers and 2 warriors on that road. If you can get this going with multiple civs, you get everyone's tech the turn it happens and can trade to the other civs and either make them broke, taking them out of the tech game, or leave them behind.
(b) Use pillage trade route on military alliances. This can break profitable trading relationships with AI, slow down their teching as they over-build units, or even take out rivals. Also, it keeps the military ally (ex ally after you pillage) favorably disposed towards you, since you are at war with the same enemy.
(3) Great Library. You can build it on Sid by doing Writing - Literature and pre-building as soon as you possibly can. Zero tech costs and the ability to generate money from tech arbitrage.
(4) Armies. The fact that Civ 3 AI won't attack healed armies makes you invulnerable once you have a Military Academy.
(a)
@Spoonwood has a great plan for generating MGLs - leave your capital undefended to encourage invasions, and then enough catapults to redline any attackers and vet units become elite become MGLs.
(b) The
@Sir Pleb funnel of deception is a way to make the wars manageable. Just ignore their armies in the field and take their cities while their troops shuffle about. No cities means no more units. Once you get the Funnel of Deception working, they really do leave very few units in cities. I found 3-5 to be pretty consistent. That means you don't even need a huge artillery stack or offensive force. If you have Cavalry Armies and railroads, it is possible even to skip artillery against rifleman-only opponents and just take out their cities in rapid succession. I took out the 4 northern Egyptian cities in one turn without a single artillery shot. I did investigate those cities to confirm that they were lightly defended.