If I recall, STR does absolutely nothing for Titan/Ifrit. Their damage output is calculated from INT, along with DET and CRIT. Judging from the video, even if Spell Speed does affect Garuda it wouldn't matter because the difference is so minimal. You seem to lose damage from stacking Spell Speed over the more weighted stats. A nice find, but the end result is the same: Spell Speed sucks.

If you're thinking of using one set to summon and then switch to another for your own damage it won't work. The pet's stats are recalculated every time Rouse, Spur or Enkindle is used.