It's a bit unforgivable to respond this late, sorry.
I've kept the gyro-concept alive until a few days ago. I've build a new kayak and have the same problem again, with the kayak getting a rest-angle to the wind off perpendicular. I went over the physics and practical circumstances again and reached your exact presentation of the problem. This new kayak behaves even more odd on the water, so a proper understanding of the problem was urgent. I've now added a rudder, so, instead of being blown sideways up upon the beach ,I now find myself racing downwind in speeds never seen on 'my' kayak before ;o)
Thanks for your respons.