I personally found it to be one of the easy Overdrive/Weapon sets to get, comparatively. Tournaments and league reset prizes fairly often, so if the prize you need doesn't show up (which they should, because they get priority over other prizes), just reset the prizes. It shouldn't take more than 20 games.

Your strategy is fairly common among those who bother to play Blitzball; it's known that Brother is broken OP because his speed stat rises so much faster than the other options. Compare, Tidus with a top speed of 73 at level 99, and even then he is one of the lucky ones who even gets a growth in speed. You're actually wasting time trying to get other people to score, just score with Brother 3 times, and then pass the ball to your defenders for the next 4 minutes so that they get the same amount of EXP.