Thanks so much for the tips on mayonnaise without soy.
Right now we are using Spectrum Naturals Canola Mayonnaise, although I got some comments for some possibly cheaper options when this jar runs out. I think I bought it at PCC Natural Markets.
So in addition to being soy-free it also appears to be gluten and dairy free. I'm thinking chicken salad or potato salad or egg salad. Maybe I can use some lettuce leaves (from our CSA) for the "bread."