I am going to make a list of things that can make skilling GS much faster. Obviously they are just suggestions and some of them might not be feasible for you, but doing any of these will decrease the time you need to cap GS.
1) Use skill up food as you mentioned. (Elshena caps at 320, you might find you have better luck using Montagna)
2) Prouesse Ring and Terminus Earring (getting either or both of these might be more of a time sink than actually skilling up, but you can always try skilling up in Zeruhn mines to get the ring out of the brown caskets).
3) If at all possible, skill it using WAR and pop retaliation and defender. Skill ups are largely about the number of swings you take per amount of time. I skill everything on WAR because retaliation can get skill ups and every time the mob hits you, you have a free shot at a skill up. And fighting 2 mobs at much means 2x the chances etc. Retaliation = free swings that aren't on a delay timer.
4) "Rent" a Mercurial Greatsword. Expensive to buy but you can always resell in a few days for minimal to no gil loss.
5) Skill up in Abyssea on DC mobs using Regen/Defense Atmas. It's been awhile since I did this so I forget the specific names, but they can be looked up pretty easily on a wiki. #5 also makes #3 more potent because you can fight several mobs at once which increases retaliation. You basically become a skill up mill. Sometimes you attack faster than the animations can keep up with which is amazing considering it's a 2H weapon.
This type of approach allowed me to skill GS (and other weapons as well) very quickly. Maybe none of these is viable for you, but if any are, each one will shorten the time it takes to skill up considerably. If you expect to be skilling up multiple weapons at any point in time, you should consider trying to make these viable.