TCL is exactly "strongly homoiconic" in the OP's sense; one does metaprogramming by creating and evaluating strings in some desired context. It's an advanced technique, but works quite well in practice. Many years ago I wrote a complete object system for TCL, SNIT, that executes a type definition script (using TCL syntax); this produces a new TCL script that actually implements the type; and then executes this new script. It's been used in commercial products.

TCL is not "bicameral" in the OP's sense, but that doesn't seem to stop anyone from doing metaprogramming.