I was also told on the boards that the Silk Soymilk Vanilla can be purchased at the Sundries shops at the resorts, it's an 11 oz. single serve container, and the cost was $2.19.
A fellow Diser looked a couple of weeks ago for me and posted the information on her live thread. The resort that she checked was the Poly, but surely they have it everywhere.
I was excited to hear that it's offered in the restaurants too.
Our DS1 only drinks Soy also and prefers Vanilla, and we are using DME, so I'll have to rely on WDW having it somewhere.