Just throwing this out there for people that didn't realize it. While running all across East Shroud, trying to get to the FATEs before they were completed (hours of work there) just so I could get enough seals to finish my GC chocobo quest, I opened my map again to see if there were any FATEs in the zone and happened to mouse over a Levemete in Hawthorne Hut and seen 'Grand Company'! What? A GC Levemete?!? Get Out! I ran over there and low and behold, besides the supply and provisioning quests (which I knew about), there were actually battle quests I could do to earn seals. Granted, I only needed a few hundred more once finding this out, but I was ecstatic, especially noticing that each one gave me over 100 seals (compared to the average of ten per FATE, granted they would always be ending just as I got to them.
Hope this might help people that need seals for things and can't seem to garner them fast enough. They made me a happy camper. :)