Despite being omitted from the product description, the pedal spanner is also a cone spanner. It is 15mm and very flat. I found this out whilst serving the cones yesterday. The only tool that I needed that wasn't present in the kit was an adjustable wrench/wrench for the cone lock nuts(?), but most people will have this already, so it helps keep the kit lean.
I'll update the review in a few months with a comment on longevity.