I know brown sugar and things of that nature are a nono. But what about pure cane juice?
You're in that part of the state where it still gets pretty cold. The problem with feeding stuff with solids in it is the defecation factor. I didn't keep bees when I was in Jax, but they will have to release outside the hive. Cane juice will have molasses in it. Besides being cruel to moles, it will be a problem for the bees being mighty uncomfortable when they get stuck inside the hive.
That was my main concern as well.