Spell speed stats do affect pets, and Garuda is unique in that he benefits off of his own spell speed proc (chance after a critical hit).
Apparently they do not, as with 405 spell speed (+60 something from gear) my Garuda still has a 3.00s recast on wind blade....
To answer your question though, you cannot lock in the proc buff by using rouse-- that would be broken because if it were chained every minute (rouse) it would turn Garuda or Selene into a machine gun.