I like your suggestion!
It ties in with the idea of a prayer quilt and also with praying for the person that 'gives you fits'.
The praying may not change the other person but it will do YOU a lot of good! I've tried it and it helps at least give you a better understanding of the person and the underlying things (on your side) that cause you to react so strongly to whatever it is about that person that annoys you so much.
So I'll add my challenge to pray for the person as you make the quilt (or as you get up the 'want to' to actually do it!)