I've always been a little slower in the atomic/information era when I play small. However, I progress much faster in science late-game when I've invested in a few more cities. You might try it--it always works for me. Rushing research labs in 7+ cities is way stronger than 5 in my experience, each easily overcomes the tiny 3-5% science penalty if you can start them early. The key to powerful science is population and more cities = more population.
This usually outperforms a small NC approach for me. I always forget about the NC and just focus on happiness and settling early game--Building it later. Works for me. I've found that I can easily steal up the difference even if I get a little farther behind as constabularies don't come until later.
I've heard of some master players using the small approach to finish by turn 300 or so, so it's possible that with the small approach and Babylon/Korea you could do better than large, however, this has always worked fine for me against the AI on all difficulty levels.
This puts me in victory somewhere between 1890-1910 on immortal depending on the strength of the AI and how many RA's I can form. Immortal you will finish faster too due to the AI being better at science and thus RA's being more powerful. Stealing Porcelain Tower makes a great difference. Rush it if you need too. And in my experience, I'm bulbing my way through half of the information techs if I play it right due to all those Research Lab cities producing and the hubble boost.
Also, build/tech order can shave 15-20 turns off the victory time in the end. The parts are expensive so timing all the buildings and having your cities ready and buying spaceship factories can really make a difference. My order is to shoot straight for hubble. Have an engineer ready. Rush it. Double-bulb to get the tech for spaceship factories and boosters, have saved up loads of money and buy spaceship factories in all the cities that I select to immediately start building the boosters/cockpit. Turn all other cities on research. Buy some more scientists once birth rates start to flag if I have faith. Go for nanotechnology. Turn a 5th city on parts. Tech for particle physics as fast as possible. If the timing right on world congress building the international space station in this downtime is a great choice--usually better than having all your extra cities on research as it only helps a little bit in my experience. I'm usually order with wide, so I'll have my buying spaceship parts with engineers ready. Probably hurry one of the going ones to leave the parts to my 4 best. Then wait it out. Save one last engineer for the last part with particle physics and hurry immediately. Assemble and shoot. One game I was into the information era and launched like 20 turns later. Despite having a long list of techs on the top of the tree I'd been ignoring. You get a huge stream of scientists with a large empire about this time.
Here's an example of the results of a wide game and the overwhelming science output difference. I won 1906 but kept playing just to see how powerful my indian empire could become emphasizing growth in my 25 cities. Most of my cities have topped 20-pop at this point, are running every specialist, and I turned on research to add a little extra though this ended up a minor effect compared to the specialists. Turning half your empire on research through the information era is a great way to shave a few extra turns off btw. Every city that is unsuitable for building parts should be cranking out all the science possible.
This game was kinda for perks. I won years ago, but my empire was so far from its full potential I wanted to see how good it could get when all cities were working all their useable tiles and had filled all specialist slots, with a few lagging cities, this is the result. I'm also supporting the world's top military at the same time. Big would always be better if the civ games didn't end so quick. *sigh* I didn't check but I've got somewhere around 20 future techs at this point--probably more actually. With this rate they come every 2 turns.