As has been told to you, it is MUCH better to focus all your research into one tech at a time, and that's what everyone will do, so there's no point in doing it this way. In fact, you can simply change your research every turn, so you can already do what you're trying to.
However, try this: go in WB and plop down 3 cities in the middle of a grassland plain with a high population (like 10 or something - you'll need no water, forest/jungle, or hills/peaks, but put a river right down the middle to get irrigation from - they should be identical and boring) and give them sufficient health and happiness buildings and a Granary. Connect them with a Road so they have Trade Routes to each other (this will help alleviate increased costs due to population). Plop 5 Workers IN 2 of the cities, and leave the third alone. Set your production to gold and your slider to 100% gold. Give yourself the first 2-3 Eras of techs and Biology. Now save it.
City #1 is your city. Send your 5 Workers out to separate tiles and improve them with Farms. City #2 is my city. Group my Workers into a single unit and send the group to a single tile and Farm it. City #3 is the control city, which will tell us how much of a difference there really is between the two cities.
Keep this going until each city has 10 improved tiles (equal to our original populations), then go a few more turns - 60 turns should be sufficient to minimize the effects of any accidental wasted Worker-turns. If Specialists are required (pop goes over 20) assign them as Merchants, Engineers, Priests, or Citizens.
Now compare the three cities. The Control city should have a population of 12-13, your city should have a population of 14-16, and mine should have a population of 15-18. (You should also see higher-valued Trade Routes.) It took the Workers the exact same amount of time to build all 10 Farms for each city, so why is my city so much bigger than yours?
It's because I focused. It takes 5 Worker-turns to build a Farm. I built a Farm every turn and had each of those turns to use that completed Farm for population growth. You built 5 Farms every 5 turns - by that time I already had TEN EXTRA farming-turns of growth! (1+2+3+4, then at turn 5 we've got equal Farms again.)
Each of these Farms represents a technology. I got a new "tech" each turn and made use of it, while you still had nothing. When we hit turn 5, I already did 10 "things" with my 4 techs.
You can see the same effect if you put money into savings. It's far better to put $100 in the bank every month than to put $1200 in every year. Compound interest is the most powerful force in the universe! And that's what this is.
So if this doesn't convince you that your method is flawed, nothing will.
There are other ways to get what you want, but I don't know if they can be implemented in Civ or not.
One way I can think of is diminishing returns. Imagine that techs cost some small number of points (say 20-100) which must be bought for gold. 1 point costs 100 gold, 2 points cost 300 gold, 3 points cost 600 gold, and so on. Intense research costs progressively higher amounts of money. If you're allowed to spread your money around on multiple techs, it is more efficient to spread it to multiple techs, but you won't get anything done quickly. You have the option of focusing all (or most of) your research money in one area and get that tech one or two turns sooner, rather than in 1/2 or 1/3 the time.
Frex: say we have 1500 gpt to spend on research, and there are 5 techs we can spend on, and each requires 20 points of research.
We can spend all 1500 on a single tech, getting 5 points toward it, and research it in 4 turns. It will take 20 turns to get them all.
Alternately, we can devote 300 to each tech and get 2 points for each (total of 10 research points bought) and get them all in 10 turns.
Even more alternately, we could just spend 100 on each, and the remaining 1000 gold could be invested in the empire elsewhere. We'd spend only 500 per turn, get all the techs in 20 turns, and have 20,000 gold to spare for whatever other projects we had.
This also makes it fairly easy to award "free" research points for if there are other players with this tech, or prereq techs that should make it easier/cheaper to research. Or you could alter the gold cost of the research points.
Another way I can think of would be to eliminate the traditional research model.
Research happens somewhere in the background, and is determined by a system similar to Civics, by your civ's and leader's traits, what your actions are, and what broad "area" you want your civ to focus on. The player wouldn't have any idea what the next tech would be or when it would arrive, only that he could influence things toward certain goals.
It would feel similar to the Great Person Production model we see now, but with actions standing in for Specialists as the influences. Influences would include what kinds of tile or city improvements you built, how big your army/navy was, whether most of your cities were coastal or inland, how aggressively you explore/update maps/fogbust, if you assign more Citizens to Farm/Mine/live in Cottages/be Specialists/etc., and I'm sure someone inventive could come up with all kinds of cool stuff to use as influences.
Behind the veil, these actions would devote research points to various techs. If you built defensive buildings, each one would devote beakers toward further defensive improvements. If you work a lot of Farms, you might get agricultural techs. If your army focuses on Mounted units, you might get Stables sooner. If you build Libraries, each could devote points to "pure research", which could be distributed to all areas equally. The traditional science slider would be for "pure research", but you could also focus part of it. Since you have no idea what's coming next or when you'll get it, AND simply having a focus doesn't throw all research toward that area, you can still see anything happening.
Throw in research bonuses for other civs having a particular tech. Throw in a diminishing returns model. Throw in minimum/maximum research times. Throw in seen or unseen random bonuses or penalties for some variety, and no two games will ever be the same. Each person's civ will automatically tailor itself toward the way that person likes to play, and you won't see any more "bee-line for CoL" advice.
Some things could work a little like the Events system does. If you have certain things, a certain event might occur which will give you a bonus in some area. The most direct thing I can think of would be having a preponderance of Pikemen might lead to that event where each Pike gets a free Melee promotion. Stuff like that.
So those are two ideas that I think could make non-focused research work.
