The speed grip that came with my Bronica SQ works the same way: two strokes. I don't mind it, really. But now the shutter release button doesn't work so I'm forced to remove the speed grip or use a cable release. Not a big deal, but mildly annoying. I may fix or replace it eventually.
Thats a bummer. Have you thought about getting the shutter button fixed by someone like KOH's, assuming you still love and use the SQ a lot?