I have been frustrated trying to figure out when and which specialist slots to fill. There never seems to be enough pop to fill everything and keep the city growing at a good rate. Definitely something I need to master should I ever take on deity, but in the meantime I just use the auto-governor and the choices mostly seem good when I look at the city screen. I will change from default focus to gold focus (during golden ages) or science focus (iff observatory) or production focus (for the rare hard-built wonder).
Can anyone guide me on balancing growth versus manual specialist control? Can I lock only the scientist slots (as you say, they are definitely worth working) and let the governor do what they want with the others? (I think locking a single one turns on manual specialist control for them all.) Are science slots really the only ones worth working? What about after you unlock the tenant from Rationalism that lets specialist consume less food?
As long as your city doesn't take 9999 to grow to the next size, send some of those farmers' kids to school and make them specialists. Your growth will pick up again once your city levels and you can work the food tile again.
Alternatively, if you already have lots of production, go with specialist instead of a mine or lumber mill.
The scientists slots are not the only ones worth working, but IMO they should always be worked. AS LONG AS your city can grow to the next pop in a reasonable amount of time. Or it may be that your pop is capped because of a lack of food. In that case, You want zero surplus food, as much hammers as it takes to build what you need to build in order to raise the food cap, and settlers.
Naturally, your highest population cities should be working lots of specialists. In those cities, you want buildings that grant GP bonuses such as Nat'l epic and gardens. Your best city, 99% of the time your capitol, you will build all the guilds. This is really the best way, since one city can build a Great Writer, Great Artist, and Great Musician all at the same time.
In LOW production cities, you may consider working engineers. Guruism helps considerably. It is a great perk for liberty games. Eventually you will want enough food in a city to work all your production AND add engineers.
All of the above paragraph is true also for wealth and merchants.