I think that there is to different suggestions here: a.) internal tech spreading inside your empire as a nerf for large badly connected empires that just spam cities, and b.) tech diffusion/tech spreading between civilizations, so not every civilization have to re-invent the wheel separate from each other.
I think both suggestions are great! the first one seams a bit complicated but this is a computer game, so we don't actually have to make all that math ourselves, as long as the information is communicated in clear way via some new interface. A think that printing press should really make a huge difference to tech spreading, maybe postal service and Print workshop could be to new buildings that would spread techs faster (and also give you a culture bonus depending on the culture of your other cites).
I agree with Naokaukodems suggestion that different techs could spread differently, maybe divide the techs in categoires: Militaristic (which spread is incresed with barracs, and which is harder to steal), construction/agricultural/production techs which spread faster with workshos and such, and culural techs which spread faster with cultural buildings. or somthing like that.
I think that the to science buildings University and Public school could be more different, with University increasing the chance of a new tech being discovered and gives more specialsit slots, and Public school increasing the tech spread and gives a procentage bonus on great scinetis points but no points itself, and neither building should require the other.
But I think b.) - tech spreading between civs are the most important factor that is missing in the game. It is just very strange that everyone needs to invent everything from zero. I think that NukeAJS and CYZ have a lot of good sugestions. If this could be included in a coming second expansion where international trade agreements and trade routes would be a part, so should those international trade routes in my opinon be a huge factor together with geographical closeness.
And why stop at a small 15% bonus? What about +1% for every civ you met that have a that tech, +2% for a civ that you share borders with or have a trade route to, +3% if you have a trade agreement and the "free thought(?)" SP (the one that gives you beakers on the TP), and additionally +2% for civs that you have a embassy, with +0,5% bonus for every following tech (every, not just one of the following) to a maxumum of 30% for techs in the era you currently in, 50% for one era ago (maybe bot a higher cap and a 10% bonus), 75% for techs two eras ago (+15% bonus). So if a civ that you have a trade agreement with and a embassy haves a tech you would get +5%, if that civ would have reseached additionally 3 techs that is dependent on that tech would you get +6,5% from that civ, which could add up to a lot
This should of balance with higher tech costs, the internal spread req, and some kind of new bonuses to civ's that research something first. Maybe a 10 turn +10% strength bonus to all units of the that kind that new tech unlocks for the first to discover a certain tech, and some kind of production bonus for buildings and wonders (+5% for 20 turns maybe?)
an other idea would be to introduce corporations in a new expansion and being the first to research something be requirement, so if you research combustion first and have a lot of steel and oil would you have the chance to form a auto company and receive a nice bonus and a few of the unique luxury resource "automobiles" which you then could trade away a nice profit.
Maybe you could even research some techs twice/ have techs that is detours and can only be researched by one or a few, so when you have research pottery would you have the chance to research advanced pottery (which would be a dead end, not taking you a inch closer to alpha centary) and then be able to build a maxumum of three porclain workshop, and it could give you a +1 food bonus on grannarys.
Whops that is a lot of brainstorming and badly made up numbers, I guess the what I want to say is that both internal (as a negative modifier) and external (as a positive modifier) is good ideas, and if science would be less of a one man race in vacuum and more dependent on geographic and diplomacy. It could also be interesting if you could specialize your self more (by researching "advanced pottery") as a tempting choice that forces you to give up space race for other bonuses, or shorter term races to be the first one to get the +10% strength musket mans.