Haste would also grant a bonus to AC and to Attack, I believe... So that's a no-go. Maybe just giving an extra attack, if that's possible (I believe in you, Orth!).
And allowing the STR bonus is a given; come on, now. It's a thrown weapon. Have you ever chucked a shuriken? More strength behind it means more damage when it hits something, be it a wooden target, your uncle's shin, your uncle's cat... Anything.