A single addition to an OOP language could completely do away with the need for the dispatching code and make OO pattern matching simple and concise: first-class messages (FCM). By this I mean, messages sent to an object are themselves 'objects' that can be passed around as parameters.
To recap, functional languages reify the structure of data (algebraic data types), and they abstract operations (functions). OOP languages reify operations (interfaces), but they abstract the structure of data (encapsulation). They are duals of one another.
All the Exp data classes created in [1,2] shouldn't be classes at all, they should be messages that are sent to the IVisitor object implementing the pattern matching:
data Exp = App(e,e) | Int(i) | ...
IVisitor iv = ...
//the expression: 1 + 2
Exp e = App(Plus(Int(1), Int(2)));
//'e' is now the "App" operation placed in a variable
iv.e //send "App" to visitor
FCM removes the inefficient double-dispatch inherent to the visitor pattern, while retaining object encapsulation for when you really need it; the best of both worlds.
Note also how the above message declaration looks a great deal like a variant in OCaml? This is because first-class messages are variants, and pattern-matching functions are objects. I'm actually implementing the DV language in that paper, first as an interpreter, then hopefully as a compiler for .NET. To be actually useful as a real language, DV will require some extensions though, so stay tuned. :-)
[Edit: made some clarifications to avoid confusion]