This looks fabulous. Unfortunately I am allergic to eggs and dairy. What could I substitute for the mayo?

I like both the extra avocado and extra silken tofu as replacements for the mayo. I made a potato salad with the tofu once and just amped up the lemon juice and salt a bit. It was terrific!

Also, I think silken tofu would work very successfully. I saw a recipe using it once but haven't tried it. You would want to amp up the seasonings since tofu isn't flavored like mayo is with salt, pepper and lemon.

If you don't know about Vegenaise you will be happy to know that this eggless mayo substitute is an excellent product in it's own right. I was introduced to it by my egg allergic roommate. Recently praised in a Slate article. Find it refrigerated.
http://www.slate.com/blogs/browbeat/2013/12/27/vegenaise_vs_mayonnaise_why_vegan_substitute_mayo_is_better_than_regular.html

Either with olive oil or avocado or a combination of both. To find out what works best, you might try making the recipe both ways, either by halving it or making it 2 different times.