The important question is: how did you get into that desperate position of being that far behind in technology?
Maybe it's Sid? You did mention that, but I still will mention that they will sometimes go for Literature and the race to build The Great Library can get lost... I've experienced that, even with good starts and prebuilding before.
Or you play a Deity start, but don't have any food bonuses and no rivers also for your capital and inner ring? I can't say that I've tried the later, but if you don't start with Alphabet, building The Great Library might be tricky for such a start. I'm not sure though, maybe it's not so bad. I do know that I tried Emperor and no rivers recently, and had no possibility of getting to Philosophy first as I recall, but I did manage to trade my way out of the ancient ages and had better position later that it definitely wasn't close to the point of so desparate as needing to capture The Great Library to catch up.
Ok, in that case, instead of learning a "crutch strategy" that helps you fix the consequences of your previous bad opening strategy, learn a better opening strategy. Then you won't get into that desperate situation in the first place... -- So in that case this hypothetical Feudalism strategy is not needed.
Uh, someone could be playing GOTM or COTM and not have the ability to restart the map and have such an issue conceivably. Also, HoF maps can't get restarted, if one doesn't want to start a new, fresh map for some reason. Modern gamer culture with streams also kind of has the "don't reload" mentality it seems, at least if you watch people play games like Rimworld.
Thinking more, in hindsight, remember that succesison game played as the Mongols with no resources recently? Where Korea was your neighbor and the super power? You guys got to Feudalism alright. And you had a fair amount of territory just beyond your first ring and maybe your second as I recall. It might have worked to become Feudal, whip in extra military in those more edge towns, and that might have just been enough to conquer Korea before they got Military Tradition and went industrial. But, I don't recall any of us thinking through that as a possibility for that game.