P.M.
Whole-grain bread and brown rice are digested slowly and can be eaten in moderation, even if you're going hard-core on the sugar. You might consider eliminating ALL sweets, though, including honey and other sources for awhile.
I've found that only about 5 days off all sugar DOES leave me feeling good, and amazingly, my sweet tooth disappears! Some people say this takes them two weeks, but the transformation is remarkable. Sadly, I usually do start eating just a little sweet here or there after a month or three (my weakness is maple syrup), and there's that sweet tooth again. But I stayed totally off sugar for about 2.5 years once. It is doable.
(BTW, evaporated cane juice is basically just sugar water that hasn't been totally refined yet.)