Coilean
Warlord
Ugh. How is getting sub-300 turn wins even possible with a science victory? Witchcraft!
The main thing that will slow down your science game in low difficulties is getting sidetracked by marginal Wonders and buildings to the detriment of expanding your population, especially in the early game when getting your early cities big ASAP should be your only priority; pretty much nothing makes beakers better than more population. A t200-220 40 pop capital + 3-4 other 20ish pop core cities should be very doable (barring having to deal with early AI aggression), which means internal food trade routes, getting WLtK day bonuses, maritime CS allies (and mercantile CS's if happiness becomes a limiting factor), and working food tiles over production tiles (except _maybe_ when building science buildings, which should be cash rushed instead, when possible). Tradition pretty much stomps in the early game for this, but a properly wide Liberty empire should be able to catch up later on.
Probably the next most important part of finishing the tech tree ASAP is making proper use of your Great Scientists. Planting them (except maaaaybe for the first one) is generally a huge mistake. A planted early GS might bring 2500-3500 beakers in by game end, compared to bulbing them at the end for 10k+. So mostly, you wait to bulb them until the last possible turn you need them, which is mostly to get Plastics and/or Satellites ASAP (for Research Labs and the ISS project in the WC), and saving the rest to the last possible turn (be sure to know how much science is required to finish the tree, so that you can bulb them as late as possible), when you can cash or engineer rush the final part.
Proper use of the Rati finisher/Oxford can also save quite a few turns: here, I saved Rati to finish Nanotech (12kish research, which then opens faith buying 3 GS at the end.. provided you make sure to have 5k faith by then, of course), then used Oxford to finish Particle Physics after popping all my GS (another 12k research), which made them combined worth roughly 17 turns of my final turn research rate.
In higher difficulty games, maximizing RA's is also obviously of key importance, but in this game I did not make a single RA; it is debatable in my mind whether at Prince difficulty they produce more beakers per gold than saving your gold to instead cash rush science buildings.
edit: should also say, don't bother with Great Works in SV: it's better to pop GA for golden ages, and GW for culture boost (preferably 8 turns after winning World Fair, so the boost is 2* higher, making them generally worth close to 1 SP apiece), when going all out science; Musicians are flat out useless.