Why do I say biology? Because these specialist cities, at least screen shots I've seen, have had wild population. It seems like an optimal scenario would be a highly populated city. My last game I used my national park city, had a forge, factory, industrial park, ironworks, had all kinds of population overflow and a full bar of engineers running, plus extra additional GP engineer's. Plus 3 scientists, four merchants, and four artists. It worked out quite splendidly.
You sound like you are coming at this with too much of a builder perspective. You don't need a perfectly developed city. All you need are food resources. A SE is particularly strong when combined with warfare because you can quickly turn newly captured cities, often not in perfect spots, into something beneficial to your empire. All you need is food, and farms don't take time to develop like cottages.
It wouldn't have worked as well without the extra food from biology. Also, it seems like this type of economy works best AFTER constitution, or would wildly be hyped up with the Pyramids (Representation benefits this tons right?).
Yes, the pyramids are quite huge. Getting them is very much recommended, though, depending on the situation, not always completely necessary. Capturing them is good too.
Even still, you need a production city (unless you're doing one of those ridiculous gambits) to get the Pyramids.
You will still likely have production cities. You just won't have cottaged cities, with the possible exception of your capitol.
You say "run a scientist from your library." Doesn't this hamper further growth? Wouldn't you want that extra farm to grow faster, get the pop overflow, and then optimally use it?
In this case, optimally using the population is the specialist. You only really need to grow as large as necessary to run the maximal number of specialists. This may and likely will be under your potential maximum population otherwise, since those specialists aren't generating food. The number of specialists you can run will be limited by the number of high food tiles you have, and potentially by your buildings if not running caste system.
I will try this out in my next game. Should this be run in the capital?
That depends on the strategy. Some people will cottage over the capitol, and run bureaucracy in order to generate wealth to sustain their cities. Others will make sure to have cities running merchant specialists, and build gold multipliers in those cities. Gold multiplier buildings in non-merchant cities aren't quite so useful, as those cities will be generating a trivial amount of commerce. You might still want things like grocers for health (more specialists) or banks to be able to build wall street in a merchant city. Science multiplier buildings can still potentially be useful in merchant cities if you are running representation, but they aren't crucial.
In general, you want to build as few buildings as necessary in your cities, so you are working specialists as long as possible. Ever touch the culture slider before? It can be a very powerful tool when combined with theaters (or even better, hippodromes) in a SE. Your research is not being generated by the science slider, so the happy boost from turning up the culture slider can allow you run more specialists without needing to worry about building hammer-expensive happy buildings.
What should be a good specialist to population ratio that I should look for? Such as...if I have a city pop at 10, how many scientists should I run?
You should be running as many as you have the food to support. Running specialists is the entire point of all but your production cities and potentially your capitol.
As for leaders, my favorites for a SE are Lincoln, Frederick, and Alexander. Lincoln and Freddy both have very good traits for a SE, but their unique building and unit come later than one would ideally like for running this sort of game. Alex has good traits, and his building and unit are much more ideally situated on the tech timeline. If you play with unrestricted leaders, the Byzantine civilization is quite good with Hippodromes and Cataphracts. The Roman and Sumarian buildings and units would be excellent as well.
Edit: In fact, I am giving you an assignment. Play as Alex, on a small or medium sized arboria map. This sort of map is nearly perfect for a specialist economy with hordes of clumped tasty deer resources, occasional seafood, lots of farmable land, and plenty of forests to chop for those important buildings.
