I doubt this will (ever) be implemented, at least in this mod, but I can't help myself; it seems like a really cool idea!
The basic premise is figuring out how to integrate (in real-world terms) the 'Great Man' theory of history with the 'social environment' theory. On the one hand, for instance, yes, calculus was certainly 'in the air' during the early 1700's, but it still took Isaac Newton and Gottfried Leibnitz -- two of the great minds of the age, if not of history -- to actually discover it.
My proposal is this: disregard all the usual rules for technological advancement. Everything that currently is allotted to 'beakers' for research goes into what is now classified as 'great person points.' This includes libraries, monasteries, universities... but also markets, banks, temples, forges, theaters, etc. (I have no idea how this might mesh with the current system for commerce, but give me time and I'll think of something).
Anyway, each of these buildings would provide some amount of GPP. The GPP from every city currently connected (cf. trade route symbol) to your capital would be lumped together and go towards a progress bar before your next Great Person is spawned. The current mechanic for how probable that GP will be a Prophet or Artist or Engineer will stay the same, but a similar mechanic will be applied to determine in which city the GP will spawn.
Finally, and this is the biggie, the GP progress bar will be probabilistic, not absolute. Say the next GP benchmark is 1000 GPP, but at the moment you only have 400 points. That would still give you a 40% chance of receiving a GP at the end of that turn. Given that this would apply at the end of every single turn, very rarely would you ever actually fill up the progress bar before getting a new GP.
Once you have a Great Person, I'd suggest expanding the options available to you. Instead of being limited to a single tech choice, perhaps you could be offered a range of options, depending on the existing system of pre-requisites. I'd also suggest tying in my previous proposal related to 'great projects' -- a catch-all term for anything that can only be built by a Great Person, rather than in the course of a usual city's production. I'd suggest expanding the list to include things like 'Gutenberg's Press' or 'the Magna Carta', but you could also swap in a few existing Great Wonders or National Wonders if applied. This would force players to choose between pursuing ever-increasing levels of tech advancement (to allow their cities to put the newly discovered techs into practice) or special wonders/projects/events that get the most benefit out of the techs previously discovered. Use your GP to speed through a bunch of techs to get a more advanced wonder, or use the GP to get an earlier wonder and risk having a rival move to the front of the queue.
Another major element would be the tech diffusion and/or espionage mechanics. Take the example of the telescope. The earliest patented version we know of dates from 1608 in the Netherlands, discovered by a man named Hans Lippershey. Within a year, Galileo was inspired to design and improve a similar device, and was soon showing it off to the scientific community in Italy. Even if you're familiar with the degree of European monoculture during the Middle Ages and Renaissance, this is still a remarkable rate of diffusion.
I would like to see a tech diffusion mechanism that increases the chance of receiving (or providing) techs based on shared civics, trade networks, physical proximity, years of peace, etc., while decreasing the chance of tech diffusion based on war, distance, disparate culture (via civics), and degree of governmental centralization (the more centralized, the more easily something can be deemed a national military secret). This latter element would be counterbalanced by espionage points -- the more infiltrated a nation is, the more easily a tech can be stolen. (This would also tie into the earlier dilemma -- go for early wonders and hope tech diffusion helps you keep up, or pioneer the field to be more sure of even better benefits from techs down the road).
In this proposal, Great People would be far more common than they currently are represented in the game. This is because they would not represent that pinnacle of human achievement -- the cream of a civilization's crop across all the years of its existence -- but the more typical geniuses of humanity who represent the best that time and place have to offer, who are shaped by society to drive society forward. The current system using Great People as stand-ins for geniuses like Isaac Newton (who, you know, discovered gravity); this system would have them stand-in for more common geniuses like Henry Cavendish (who measured the gravitational constant for Newton's equations).
I figure this whole proposal would be way too extensive to actually see everything in action, but even so, I'd love to see some of these ideas applied to this or other mods.