OK, after 10 hours of play, I finally managed a turn 304 science victory. Not the most optimal play, for sure - I made several blunders like missing Colossus and not making enough workers early on (or any point in the game, whoops).
First of all, I want to say that this is not a good map for learning the basics. It's too big, which means that you won't be able to get a feel for what you usually want as a build order; instead, if you play to win, you'll be out spamming settlers and workers far more than you usually should. Also, it doesn't teach you to carefully expand without crashing your economy, because on huge maps you can spam settlers everywhere and barely feel a dent in terms of city maintenance. Second of all, the resources available here are terrible. I wasn't able to switch off hereditary rule for the entire game because I needed stacks of units in every city just to be able to grow to size 12 and beyond. The only happiness resources you have remotely close to your start are ivory, gold, and sugar, which won't cut it in actually getting your cities to grow, so you had to pursue some unorthodox strategies in getting that happiness (such as the aforementioned HR unit spam). And finally, oh god, the barbs. Because of the sheer amount of unclaimed land in the early game, forget about spawnbusting. You need a fairly sizeable military to not only defend your cities, but proactively stomp out any barb axes, swords, or archers who would otherwise go around merrily pillaging your everything. This type of thing is definitely not orthodox in most other games.
Now that my rant about why this map is bad for learning is out of the way, let's see what you should've done. First of all, upon opening your save, I saw that you had 15 cities. This is NOT enough. I told you that you needed 15-20, but that was for a STANDARD map. For a HUGE map like this, SPAM cities. And I mean SPAM...if you have less than 30 by the end of the game you're not doing it right. It doesn't even matter if they stay at 1 population; as long as they're hooked up and have a couple trade routes, they should more than pay for the commerce that they consume...because on huge maps, maintenance is LAUGHABLE. You can found a city literally 20 tiles from your cap and it'll cost, like, 2 gpt, max (if it's your 5th city, even). Of course, that does not mean you shouldn't develop your cities - workers are important too, and keeping a 1.5:1 ratio applies as always. And don't build just settlers - remember to granary and forge up. Libraries are also especially appealing, because as a creative leader, they give a pretty cheap +25% science.
On the subject of trade routes - GLH is a GODLIKE wonder on this map. Seriously. Building it will decrease your win time by AT LEAST 50 turns. The +2 trade routes per coastal city is very OP when you're doing nothing but spamming cities (most of them should be coastal anyways), and Egypt/France gives cheap intercontinental trade routes which are +100% boost to commerce. Oracle is nice too, though because of the tech path you'll probably be forced to take currency or CoL with it instead of civil service, because that's just too late. But, again - GLH. Build it. Let's do some math - say you have 10 cities mid-game, 8 of which are coastal and large size, and they each get 2 extra trade routes each. That means +6 commerce at least, probably, in 8 cities, which translates to a big fat +48 commerce per turn, BEFORE MULTIPLIERS, JUST from GLH. If you found a city on the coast, it'll instantly get like 10 commerce but cost maybe 3-4 gpt in maintenance, at 1 pop, before any building is built whatsoever. GLH is so broken here that you want to avoid corporation as much as possible, just for the trade route boost (when I researched corporation, I went from 1400 to 1300 bpt...).
Speaking of commerce...this map is especially commerce poor. There's, like, 2 rivers which are within settleable range...and by that I mean both are more than 10 tiles away. What you're going to want to do is to rely on coastal tiles for commerce. As financial, building a lighthouse instantly makes them 2 food 3 commerce tiles, and with a dike, +1 production as well (Dutch FTW) - this is a pretty good tile to work. So what you want to do is strategically spam coastal cities near seafood resources. This will allow them to grow pretty well, while also rake in the commerce almost without needing a single cottage. Improve the nearby tiles...split flatland 50/50 between farms and workshops, and mine hills in food-rich cities while put a windmill on hills in cities without nearby fresh water or food resources. Later in the game, as you taper down the settling and the barbs start to disappear, start building wealth and research. Try to pop a few great merchants to do trade missions to fund your research. Again...academy in cap first (the GS doesn't have to come from the capital, thought), save later GP for golden ages, which the MoM (can't spell that...) helps greatly.
As for dealing with the happiness and health issues...try settling the other continent, which has corn and rice for +4 health (with granary) in every city. Besides hereditary rule, I don't see another viable solution for the happiness problem, though. This particular map script is really mean in this regard. I should've conquered someone, but I was too lazy to do it, and it would've taken just so much extra tiiime.
Tech order - you'll want to juggle sailing, masonry, priesthood, and mathematics, in that order, for a combined GLH + Oracle strat. Pick up calendar afterwards to improve the bananas and sugar. Then, go civil service for bureaucracy (maybe even feudalism first for longbows against the barb sword/axe rush, and to tech civil service faster). Next, go with guilds, for grocers, knights, and everything that comes before (workshops and forges at metal casting, the mills at machinery). After that, rush communism, preferably with astronomy; I used liberalism on communism this game (how fitting, heh). A GS or two to help bulbing really makes a difference here. Communism will allow you to spam cities at full throttle, and also combined with caste system makes workshops arguably the best standard tile on this map - never underestimate the power of building wealth and research. Use the free great spy to get a golden age to eliminate the anarchy wait, and then switch to those civics, as well as free religion (from slavery, of course, which is what you should be adopting in the early game). After that, I went assembly line, hitting the dreaded corporation, for factories, and then biology, industrialism for aluminum, and finally rocketry for Apollo Program. After Apollo, I went superconductors for labs and boosters, fusion to start on the most expensive SS parts first, genetics, satellites, composites, and cleaned up with ecology. I used the GE to build the Three Gorges Dam, saving me the hassle of building like 30 coal plants.
Overall, a very fun map, if not what I expected. I was slightly miffed that I missed the sub-t300 by 5 turns (I blame random events, which hated me this game). Despite the very peculiar map, some of these tips still apply to standard space games - mainly the communism rush, GLH strat if you have a lot of coastal cities, and the process of actually founding enough cities so that you won't be squeezed in. The mark of a good civ 4 player is being adaptable, and I felt like I was in this game, at least somewhat. So...there you go.
PS: I have, like, 12 hours of recordings of me playing this map, but I'm sure you wouldn't want to sit through me thinking for 12 hours. And at any rate, I don't feel like uploading all that. But, attached are final screenshot and save. If you have any questions, feel free to ask!