For science victories, rather than focusing on the Education turn times, I would start by focusing on population goals, as science largely comes from population. Pick a turn number that is not a full game length, and try to maximize your population by that turn. For example, try to get 20-25 citizens by turn 100, maintaining positive happiness for all but a few turns. Then step it up 25-30, 30-35, etc. Then, try to get a 10 pop capital by turn 100, a 12 pop capital, 15 pop, etc. If you hyper-focus on chasing every little beaker number too early, you may actually end up in a worse position than if you had just focused on population. For example, assigning a science or culture specialist in a city before the city can support that specialist will stunt your long-term growth. The great library might sound good, but might have to give up too much to get it, especially on higher difficulties, so you need a clear reason for building it.
Culture, gold, production, wonders, and religion can all be used to accelerate growth. Once you become good a growth, than add in additional goals for things like beakers, or rush-buying science buildings, or faith accumulation for late-game, or being ready to open Rationalism at renaissance, etc. Early education turn times will just happen once you become better at growth. Solid population growth is at the core, and these other things are additional layers that reduce win times further and further.
Another goal I go for is to settle my core cities by a specific turn number, try to lower that turn number step by step. Or alternatively, settle your pre-National College cities by a certain turn number, and then find a way to have the last settler(s) ready the moment the National College has finished. Future cities do not grow, make buildings, or build units now. Founding a city early gives it more time to grow. This is even more important on Deity, but I find that it is essential skill for nearly every victory condition. Generally speaking, a really good science player will NOT settle cities after a certain turn number, even after National College, because there is no real benefit vs. aggressively taking one, or focusing on something else. For other victory conditions like Domination, there are times when it makes sense, but there is a cutoff point for a science victory.
When I first started playing Immortal, another way I improved was by playing the exact same map save several times, up to a certain turn, just to experiment with what worked and what did not work for different maps. I think a good player learns to spot opportunities and take advantage of what each map offers to the player, rather than going into the game with a pre-determined build order. I would recommend boldly and aggressively exploiting every opportunity available, rather than following a pre-determined strategy.
Another thing I figured out was that a really skilled player will have the same capital you had on turn 150, but build it by turn 100. In other words, unless Petra is involved, there is no secret building or secret wonder in the city, the best players took advantage of everything available (city states, neighbors, diplomacy, trade routes) to build the exact same city in less turns. So, most of the time, you can't look at a snapshot of the final turn and figure out how they did it. I had to watch some of the LPs out there closely to figure it out.
I would also highly recommend NOT switching to Deity if you are not ready for it. If you always win Emperor, then try Immortal. If you always win Immortal, then try Deity. Deity is easier in BNW than pre-BNW, but starting next to certain AIs like Attila or Dido on Deity difficulty can be immensely frustrating, and will definitely interfere with your goals. You may not survive until turn 100. On Deity, the Maya might build the Oracle on turn 55
The ICL/DCL series might also be useful, especially if a more skilled player has recorded a video of the same map that you played. Figure out what they did better, what you did better, what tricks they used.
Hope that helps, and good luck on your sub-300 science victory