There is no way to produce sugar.
Radishes have no rare drop whatsoever.
=> Give radishes a rare drop much like spooky redcaps/jalapenos- SUGAR BEET
=> Add a new skill "Sugar Production"
=> Sugar Production skill gives you acces to the sugar beet drop and also a new building "Sugar mill"
=> The sugar mill can work as the oiling press, you just have to fill it with milk of lime
=> Place the sugar beets in the mill and turn them into sugar.
Can be done in a more complex way tho, Im just giving a basic idea. (Just want to say I liked the mistery of cheese production and I hope we get more things like it)
Lazy method:
=> No skill needed, you can slice the sugar beet by right clicking it and picking "Slice", this will yield you some sugar beet slices or "cossettes"
=> Select a slice, right click it to a milk of lime bucket and it turns into sugar, using some milk of lime from the bucket
So now we have rare drop from planting radishes and also a way to produce sugar at home.