I was intrigued by this map, so I wanted to have another go to see if a faster finish time would be possible. Indeed it was, I got a T151, altough it was not a valid attempt: I reloaded for two same-turns on early wonders, which was also the weak point of the play I was attempting, as I will explain shortly.
I actually started the map a couple of times, and tried to get a good start, but raging barbarians made it difficult, even on Prince. The first 30 turns are ok, your scouts can roam free and pick up lots of ancient ruins, but once more camps show up and fill the lands with barbarians, scouting became almost impossible (in my second full attempt I again did not meet all the civs, despite my map knowledge), unless you radar very carefully perhaps, but I would find that too tedious. I even played around with opening honor, to help locate the camps and to get the 33% combat strength help for killing them, but even then, on quick speed, it takes two units to clear out a camp.
In the end, I defaulted to what worked well in the Celts game: Liberty with a splash of tradition for wonder building (and border growth), and then into commerce. I think what went well this game was to go almost straight into settlers, something like scout-buy scout-scout-monument (I wanted actually scout-monument, but out of tradition, no pun intended, I created a second scout)-worker-buy worker-followed by 7 settlers, and only then worry about wonders. This really helped getting out my cities quickly and set me up for a good game, but of course by that time the AI is starting to complete wonders too.
After the settlers I went granary into Temple of Artemis, but I got same-turned (I know, it's not really a same-turn, but it does feel that way if you have one turn left and the AI completes the wonder over the end-of-turn) by a far-away land. So, I reloaded, skipped the granary, and this time got the wonder. After ToA I saw that Great Library was still there, even though France had been building it for some time. I declared war on France and started the wonder, but I got same-turned again. So, another reload to bribe Rome to also declare war on France, and this time I did get the wonder. Perhaps I should not have bothered with either wonder, knowing there was a chance I would get beaten to them. An alternative was to build either of those wonders before settlers, while 'waiting' for Collective rule, but I felt that would have slowed down the game quite a bit. Getting the settlers out first was the greed play, but of course you have to be really lucky to pull that off, or cheat, or both.
Getting my cities out early did mean my one of my coastal expands (one more this time) could build Colossus early. Other early wonders that I was lucky to get were Mausoleum and Machu Picchu. From that point on, the game was quite straightforward: I went Industrialization first again, and engineered Big Ben - I still spawned a single engineer this game, which I could not avoid with Temple of Artemis and Petra in the capital - and delaying universities until after workshops and aqueducts, though I'm not sure going unis first would have 'saved' me. I considered Order, but ended up going Freedom again anyway.
The end game was good, though it still showed there was room for improvement. I missed spawning my final scientist because Porcelain Tower finished a turn early due to city growth, and by the end game I had more science than gold and culture; I had researched two techs too many, but also fell 50 faith short of buying another scientist. In the end, culture was the most problematic. Also, I had not finished Liberty since I wanted to do that during a natural golden age, but I did not get my first one until T120! The challenges of going Liberty I suppose. As it was, I finished Liberty only in the last turns, for an extra scientist, though that was actually a mistake, since now I had to wait two turns for Spaceship Procurements.
To conclude, I think if I were to have the game of my life I (including cooperating AIs that don't build my wonders), then a sub-150 might be possible, though ~T133 would be beyond me. Final note: in all of my attempts I insisted on founding Kitzbuhel, because the lands were so lovely, but actually it was a bit too far away, and the borders took too long to grow to all the wheat tiles. Also, that is the city that did not spawn its scientist.