[hitchstory]

>my understanding of the problem only really forms through writing code and seeing what approaches work.

Unless you are working with a new/untested technology or approach (i.e. you need a spike), the same kind of understanding should form while writing the test scenario.

>Maybe this should be a separate prototype phase

I always either spike (in which case I never TDD) or write production code (in which case I always do). I can't under what circumstances anybody would want to convert spike code you based out as quickly as possible to prove a point into production code.