I read last week about an Australian researcher using honey as a base to make graphene. Can just see people keeping bees in their backyards to create base material for their future printers...
I hypothesize that that technique will not work. Graphene molecules are flat, only 1 atom thick. So while they are strong in 2 dimensions, once you start stacking graphene vertically, it's just like a stack of paper. The layers won't be nearly as strongly bonded vertically as they would be along the plane of graphene. I think you would end up with a product the cleaves easily along the layers of graphene. I'm pretty sure you going to need a 3 dimensional arrangement of atoms.