I've considered even using KNO3 instead of NaNO3 (and may try it in a day or two) as the potassium is a "spectator" ion. Even other variations and modifications of the Hummer's method include using concetrated nitric acid (nitronium ions), with fuming sulfuric acid to oxidize the graphene.
Interestingly, NaNO3 is not just an oxidizing agent. If you change it by another oxidant, the number of carboxyl groups would change dramatically, therefore more sp3 are formed. Replacing with KNO3 gives also NO3- ions but remember, KNO3 forms explosive compounds, therefore K ion is not merely an spectator, the hydration sphere around it is very different than around Na+. The same applies when using concentrated nitric acid, it tends to form explosive compounds with metal traces... On the other side, the KMnO4 quantity influences the degree of oxidation indeed.