I am certain Central of Georgia box cars, without doors, were used in lime service. I have taken, but not found, photos of either CG or Southern cars carrying lime but I will keep looking. The Hayne Shop records show some 50' cars in lime service but they may have been roof hatch cars.
One reason why I sure 40' cars were used is because seeing box cars with no doors was unusual. There is no official drawing but the Central applied a small (3" letters?) stencil to the right of the door that said something like "lime service, no doors, do not bad order".
Bulk fertilizer or untreated hides ("tankage") were supposed to be shipped only in the lowest class box cars as they contaminated the car. Box cars at that point were one step from the scrap line. As no "modifications" were done, there are no shop records or car assignments that tell us which cars were in that kind of service. Given the condition of the cars, I suspect they were not in that service very long.
I am not aware of box cars being used for pulpwood although "never say never". While shortages of wood racks were not uncommon, unloading facilities at mills would have had a difficult time dealing with box cars. Even with inexpensive labor, the time to load and unload box cars by hand would have made it uneconomical.