As always feasibility ain't my field (I just throw the idea-rocks around), but hows this concept: you have largely seperate but occationally interacting tech trees in several different catagories (philiosophy, economics, natural science etc.) and they each have a funding level that can be adjusted with a subset of the science funding slider. Overal science budget would be divided between the catagories and the trees would run largely simultainiously (so you could discover several techs in a single turn). You could make the trees blind for increased realism and introduce tech 'choke points' where development in a particular field will come to a halt until a particular threshold in another field has been reached (for example, your physicists can put together a coherent theory regarding electricity but until the development in engineering allows for a capable generator it can't be tested practically).
If the trees were blind you would be able only to specify a broad field to focus on (for example military strategy and tactics) and could recieve 'unintended' benefits form research in an other field (like gunpowder that would be a byproduct of the natural sciences). This would remove beelining and help discourage over-specialisation (you could dump all you funding in tactics, but if you neglect the natural sciences you'll quickly end up with a well trained but poorly equiped army).
This could be tied in to the early suggestion of more specialised tech bonuses from certain buildings (I always thought it was odd that an observatory would help me get to military tradition quicker but all my barracks had no impact). Some buildings would be very specialised (barracks, observatories, banks) and some would boost the overall science out put of a city (library, university) and as time passes and the player finds their tech priorities change, they will be rewarded for encouraging balanced development of tech buildings and specialisation by city (the effects in any one field being cumulative across a city).
Probably a bit complex to impliment, but its a thought...