Tried again with an improved strategy (and luck) and got a
T97 win 
Gameplan and gameplay writeup
I know, I said I would not try again, but I just really liked this gauntlet and wanted to get a sub T100 win soooo much. Also I checked
@Manpanzee's game log and it inspired me to go with a very warlike approach - basically I DoWed everyone everytime I saw they had any money or anything else valuable to give. And I went almost only units except the mandatory Shrine/Monument/Temple, so I had way stronger army than anyone else very soon and was able to get very good peace deals repeatedly. Also I had a very lucky start of course. First I found Barringer Crater T0 (6 tiles from my cap) and insta bough a Scout and a Worker. Then also found Lake Victoria on T7, 9 tiles from my capital. Then I also found Mt. Kilimanjaro on T16, but I was still first to find it, even though it was just 7 tiles from Copenhagen and 26 tiles from me. Quite far, but I still sent a Settler there and founded Cordoba on T42 (the journey of the pilgrims was tough, had to accompany it with 2 units). Also I delayed my Religion for several turns so that Cordoba would receive the One with Nature pantheon. Then later in the game I also found the Grand Messa on T52, I wasn't first to it obviously, but I still immediately bought a Settler and founded a city there, as it wasn't super far from my capital either, 17 tiles. Also as I was keeping almost everyone in check by demanding everything they had and not letting anyone complete any CS quests etc., they weren't able to get much culture - it actually resulted in the best AI Carthage (they were far from me) to pile up only 680 culture till the T97, while before in my mostly peaceful games the best AI would usually have around 1000 by that turn. The only problem was that I wasn't able to find Maria I of Portugal at all. It was turn 82 and I had like 90% of the map scouted, but still no sign of Maria. I already knew she must be in the top right corner, but I only had 1 Spearman there with 30% health going through very ugly terrain seeing barbarians left and right. And to get to this part of the world one had to go all the way to the bottom half of the map because in the top there was a huge mountain range and a lake. So yeah, I was getting fairly desperate. Luckily my heroic Spearman somehow avoided the near certain death and prevailed to find Maria hidden behind the huge mountain range in the very top right with just her capital. It was turn T86 and she had not met any other civ yet. The only one somewhat close to her was Carthage, but that only made things worse as Dido expanded a lot and was blocking my path making the journey even longer. Of course I took every last penny she had for that insolence! Well anyway, the gods stayed on my side and I was happy to find that Maria certainly isn't a very cultural person, actually she was the biggest barbarian of the lot with just 337 final culture. Guess being alone in the woods and mountains cut off from the rest of the world doesn't inspire people culturally too much. Other than that everything went smooth, I was raking in over +100 Faith per turn since like T80, so my Tourism kept rising steadily. There was only one minor obstacle - Dido of Carthage, the cultural leader of the rest of the world (still pretty much cavemen level) wouldn't accept any of my gifted cities. Or more specifically, she would accept them and then burn them to the ground immediately. I tried twice, first one I admit was a sh*thole of a city built specifically for her in a north-Canada-like area (just snow tiles around), so I tried again with a much nicer riverside city close to a wine yard. She burned it to the ground the second she got it anyway. So I decided I have to give her something she can't burn to the ground and sent Gandi to his next live (he probably became some insect though as he wasn't very nice this game at all). Dido paid me all she had for Delhi, but instead of keeping it she immediately brought Gandi back to live with some dark magic of hers. So no, there wouldn't be a trade route between our civilizations this game. If there was, the Carthaginians would probably have accepted the Spanish cultural domination some 2 turns sooner, but oh well, I guess Spain can't complain about a 450 BC cultural domination.
Notable events
T00 found Barringer Crater 7 tiles from my capital (ehm, Settler, there was no capital yet)
T07 found Lake Victoria 9 tiles from my capital
T16 found Mt. Kilimanjaro 26 tiles from my capital, and only 7 from Copenhagen; still 1st to it; also Barcelona was founded near Lake Victoria
T19 started worshipping the Nature gods and all Natural Wonders became holy places that inspired a lot of faith
T37 the long expected Great Prophet was finally born; he decided to enjoy life for a while before starting his religious agenda though
T38 Seville was founded next to the Barringer crater - just a small village in the wilderness for only the most devoted
T42 finally the pilgrims arrived to the mythical Mount Kilimanjaro, and established a settlement called Cordoba there
T43 the Great Prophet finally started his Religion, a turn later than he should have, the lazy bastard
T48 Philosophy was discovered and people learned how to build temples
T52 the Spanish archery batallions randomly stumbled upon a mythical mountain called the Grand Messa. Apparently some local pagans found it first, but still the brave soldiers found a bit of gold there, and gave it to their mighty Queen; she immediately sent a group of pilgrims to establish a spanish settlement there
T59 and a bit later they did, and called it Toledo; they started mining gold there
T61 another Great Prophet was born, and this one was way more devoted and immediately enhanced our religion by teaching people how to build Mosques and also how to train missionaries cheaper
T64 Spanish Sacred Sites started attracting tourists
T70 Gandi realised that Mumbai would be better off belonging to the Spanish empire; it is possible those 6 legions of Spanish crossbowmen helped him with his decision
T85 Queen Isabella decided to help teach the pagans from the Carthaginian empire the true ways of God, and established a nice little village called Pamplona for them; pagans sticked to their pagan ways though, and burned the village to the ground
T86 the brave Spanish explorers went beyond the edge of the known world and found a remote and very uncivilized nation who called themselves Portugese. These indigenous people had not met anyone from the outside world before, so they were a little hesitant at first, but quickly they realised the Spanish culture is good for them, and started buying our blue jeans and listening to our pop music
T94 seeing how the Indians struggle without a proper leader, Queen Isabella took over the city of Delhi and after seeing it, she decided this might be where the Carthaginian pagans could learn to live civilized lives before they were ready for the real Spanish culture. The pagans used their dark magic though and brought Gandi back to life
T97 the Spanish culture became dominant in every corner of the known world, even at the Carthaginian pagans. It took a bit of persuasion and a razed city here or a few dead pagans there, but the world finally became a better place
