A Hessenberg matrix would be a special case of a banded matrix. However,
lapack has no function GBEV (for whatever reasons), so the request seems
reasonable to me. A binding for TREVC should already exist.

You are right, after double checking there is a binding for TREVC.   

I would not object if Jeremy wants to implement the missing bindings
himself, but I certainly want to encourage him to use the bindings
library. So I would be willing to implement the requested bindings.

I'll spend some time trying to implement the requested bindings.  I'll feel like I have contributed something.  If I get stuck, I'll ask and hopefully not bog down this mailing list :D.