Translating the code from How to create a SerializationBinder for the Binary Formatter that handles the moving of types from one assembly and namespace to another into very quick n dirty c++ cli, we get something like
virtual Type^ BindToType (String^ assemblyName, String^ typeName) override
{
    auto m = Regex::Match (typeName, "^(?<gen>[^\\[]+)\\[\\[(?<type>[^\\]]*)\\](,\\[(?<type>[^\\]]*)\\])*\\]$");
    if (m->Success)
    {
        // generic type
        Type^ gen = GetFlatTypeMapping (assemblyName, m->Groups["gen"]->Value);
        List<Type^>^ genArgs = gcnew List<Type^> ();
        for each(Capture^ c in Enumerable::Cast<Capture^> (m->Groups["type"]->Captures)){
            Match^ m2 = Regex::Match (c->Value, "^(?<tname>.*)(?<aname>(,[^,]+){4})$");
            String^ tname = m2->Groups["tname"]->Value->Trim ();
            Type^ t = BindToType ("", tname);
            genArgs->Add(t);
        }
        return gen->MakeGenericType (genArgs->ToArray ());
    }
    return GetFlatTypeMapping (assemblyName, typeName);
}
Type^ GetFlatTypeMapping (String^ assemblyName, String^ typeName)
{
    Type^ result = Type::GetType (typeName);
    if (result == nullptr)
    {
        result = Type::GetType ("MyNamespace." + typeName);
    }
    if (result == nullptr)
    {
        if (typeName->Contains ("BindingList"))
            result = BindingList<int>::typeid->GetGenericTypeDefinition (); //int is just a placeholder
        if (typeName->Contains ("KeyValuePair"))
            result = KeyValuePair<int, int>::typeid->GetGenericTypeDefinition (); //int is just a placeholder
    }
    if (result == nullptr)
        throw gcnew Exception ("Fail");
    return result;
}
However, since I know which classes to translate, I found the following way easier. This way we do not have to care about nested generics either. The variable OldClassList is assumed to be a list of strings containing the classnames that have to be moved into the namespace MyNamespace.
virtual Type^ BindToType (String^ assemblyName, String^ typeName) override
{
    String^ newTypeName = typeName;
    for each(String^ name in OldClassList)
        newTypeName = Regex::Replace (newTypeName, "(?<![.\\w])" + name + "\\b", "MyNamespace." + name);
    newTypeName = Regex::Replace (newTypeName, "\\OldAssembly, Version", "NewAssembly, Version");
    Type^ result = Type::GetType (newTypeName);
    if (result == nullptr)
        throw gcnew Exception ("Could not parse the string {0} to a valid type."->Format(typeName));
    return result;
}