I wonder if the lack of strongly statically typed embeddable languages is due to an accident or a fundamental limitation of implementations of such languages. Is the type checker code too big? Is it too complex?
Moreover, designing the actual type system is at least as hard as implementing the type checker. Coming up with a static type system that is flexible/ergonomic, expressive/powerful, sound, easy to use, and also a good match for mutable state and imperative code is really, really difficult, as demonstrated by C, C++, and Java.
A flexible/ergonomic dynamic type system is trivial in comparison. Soundness is handled at runtime when the exact value of each expression is known, and ease of use is almost a given.
It's actually extremely easy, particularly if you're familiar with Prolog (the core algorithm is a couple lines in Prolog, so knowing how that works is useful for implementing it in other languages).
I suspect the lack of statically typed scripting languages is more of a historical accident than anything.