One thing to remember is that packing for a couple of months isn't much different than packing for a long weekend. Once you toss on a few days clothes, gear for variable weather, a reasonable tool kit, and tent, etc. the length of a ride doesn't change the list much. The kitchen sink is best left at home in the kitchen.
Consider going soft. GiantLoop bags are just-right sized for extended trips so long as you keep it light. http://www.giantloopmoto.com/
They are popular with the off-road/adventure/sport motorcycle touring crowd for good reason. There is no reason you couldn't fit on on your scooter. They keep the weight lower than a box and make for stable riding. Here is a Coyote mounted on my bike.
Wolfman makes a great bag that would go well on your rear rack too http://www.wolfmanluggage.com/Tail/beta_bags11.html