You receive Auroch Reels as a first prize in a tournament after getting Attack Reels and Status Reels, as well as fighting in a total of 450 battles.

You receive the Jupiter Sigil as a first prize in a league after getting Auroch Reels. There is a 50% chance the Sigil will appear, but I use this method.

Play to the end of the current league. When the prizes have been awarded you are given the options 'back' or 'continue'. Choose 'back' and save your game at a save sphere. Next, open up the blitzball menu from the save sphere and see what the prize is in the League. If it is the Jupiter Sigil then start playing. If it is something else then perform a 'soft reset' (all the shoulder buttons + Start + Select) and reload your save untill the prize is the Jupiter Sigil.

This method is better then your idea of using the 'reset data' option because it allows you to keep your team.