There should be some way to adjust the tension on the pedals, adjusting them to the loosest position may work best for you. Assuming you hadn't tried that, that is.

I use Shimano SPD road pedals, and I can pretty well unclip at any point in the pedal stroke, on both sides if needed. Handy in emergencies! (I've not used other styles to compare, tho)
My stoker on the tandem has SPD mountain pedals, adjusted to loosest tension, but has to rotate them to a certain position to unclip. Of course, she doesn't seem to have any problem on her single bike with them.