...I wouldn't recommend sugar cane unless they're prepared to grow it as the only crop: it drains the earth of nutrients, needs a lot of space (since you need a LOT to make sugar), if you want to grow something else... I wish you luck trying to get rid of the roots since it's like a weed, you can't grow it in windy places because it will fall and, as far as I know, taking into account the time the story is developing, they only will able to cut it by hand which is a bit of a high-risk job since the leaves are pretty sharp... They can burn the fields to get rid of the leaves (never understood how they controlled the fire so it didn't consume even the cane) but then the risks of a fire breaking out in near towns will be higher...
Why not beets? It won't be as sweet as sugar and being a root it will have its own troubles anyway, but at least it won't be so hard on the earth as growing sugar cane........ Sorry for the long essay about sugar cane 🤣🤣🤣