The goal seems to be making science more pro-active by having more of it come from choices other than simple population. Because this is not something broken or even particularly unsatisfying, it is important to avoid a solution that nerfs tall civs and (more importantly with regard to overall game-play) the AI.
Lower the science per pop down to 1, add an flat science bonus to the palace (or just to the player) for initial compensation, or maybe lower tech costs (this should only be for first few techs). Introduce a set of buildings that will increase the science rate. Each of the new buildings could introduce a science per pop that would eventually stack up in addition to other effects such as science on villages. The later ones have higher maintenance and more requirements (the Natural History Museum requires four buildings) but would be more powerful than the Scriptorium.
Basically I'd rely on a combination of buffing some of the improvements with science (either directly or indirectly) and the introduction of new science buildings.
Sukritact has combined some prior suggestions, added some of his own, and laid it out extremely effectively. I call it the Jade Hall approach, and agree that, on the whole, it's the way to go. The upside is that, like the Jade Hall, new pop-based science buildings reward tall civs who focus on them, potentially creating a needed separation from the strengths of wide civs. (Wide civs are nerfed the most by this approach, as they should.)
In order for the new buildings to work as advertised, I don't think they should be expensive, simply because there are a lot of them, and there is only so much time in the game. The goal here isn't to make it harder to do well in science, but to make it a choice. (I see this as the biggest caveat to the entire approach.)
That leaves us with the question of the AI. In my current game, America with 8 cities has double the pop of Spain with 31, but the two of them are slightly ahead of my Korea in beakers on t225. This is great, and what we want to avoid nerfing. Most AI civs will not benefit from the Jade Hall approach, but... the AI builds villages to excess. So if villages gave science after reaching the Renaissance era (or tech), then a fast-growing AI would benefit more than the typical human player, but still allow a tall human civ to compete in this arena by building villages at that point as well.
Taking some version of Sukritact's construct should work, and only require minor tuning afterward.
Two minor points:
Korea doesn't benefit from the villages, but they are doing well enough, I think.
The Museum of Natural History doesn't seem like a good name for that improvement. "College" would be more obvious, even as a placeholder. Something like "Salon" may work.