(That is, the dynamic-or-static choice is a product type, not a sum type!)
Not really. "Dynamic type" just means an object that carries around a description of its structure (or more commonly, a pointer to a description). You can do the same thing in many languages with static types. (Including Haskell. GHC has special support for this pattern.)
Alternatively, you can just define a recursive sum type expressing all the possible runtime types of the dynamic expression. In Aeson for example there is a type which can encode any value which might be found in a JSON file, which is basically everything you can express in Javascript apart from function closures. This doesn't require any special support from GHC and works well in most statically-typed languages.