So after playing around with it a bit I can confidentially say that with 3x speed enabled, using the draw point at Shumi Village to get 300 Ultimas is a viable option now if you want that as early as Disc 2. Provided you completed the Chocobo Forest quest, have that character at at least 80+ magic state and also have a SeeD rank at about 18 or so since it WILL go down a few ranks doing this. Just draw from Shumi, leave and go to the near by Chocobo forest, ride it to the Chocobo Santuary on Esthar, ride that chocobo back to Shumi, and bam, it should be refilled. The 5000 gil per use should be a pittance since your SeeD rank will trigger 2, sometimes three times as you ride the Chocobo...