boost::python - Export Custom Exception (2nd edition)

Based on Boost 1.88.0, boost::python Export Custom Exception and linked discussions I'm using the following to expose a custom C++ std::exception to python.

class cException : public std::exception
{
  private:
    const std::string m_message;
    const int m_code;

  public:
    cException(const std::string &message, const int &code = -1);
    virtual ~cException() throw();
    const std::string &message() const;
    const int &code() const;
};

template <class ExceptionCustomType>
class exception_ : public boost::python::class_<ExceptionCustomType>
{
  private:
    std::string m_exc_name;

  public:
    template <class ExceptionBaseType>
    exception_(char const* excName, ExceptionBaseType excBaseType) : boost::python::class_<ExceptionCustomType>(excName, boost::python::no_init), m_exc_name(excName)
    {
        PyObject* excType = PyErr_NewException((std::string(boost::python::extract<std::string>(boost::python::scope().attr("__name__"))) + std::string(".") + this->m_exc_name).c_str(), excBaseType, 0);
        boost::python::scope().attr(this->m_exc_name.c_str()) = boost::python::handle<>(boost::python::borrowed(excType));

        boost::python::register_exception_translator<ExceptionCustomType>(
          [ptr=excType](const ExceptionCustomType& e) {
            boost::python::object excObj(boost::python::handle<>(boost::python::borrowed(ptr)));
            excObj.attr("__repr__") = boost::python::str(e.message());
            excObj.attr("code")     = boost::python::object(e.code());
            PyErr_SetString(ptr, e.message().c_str());
            PyErr_SetObject(ptr, boost::python::object(e).ptr());
        });
    }
};

BOOST_PYTHON_MODULE(MyModule)
{
  exception_<cException>("MyCustomException", PyExc_BaseException)
  ;
}

In Python then this works like this:

import MyModule

try:
  MyModule.throw()
except MyModule.MyCustomException as e:
  print("REPR = ", e.__repr__)
  print("CODE = ", e.code)

But I don't like it that the attributes "__repr__" and "code" are set in the register_exception_translator. I would prefer to set them in the python exception definition itself. E.g.

BOOST_PYTHON_MODULE(MODULENAME)
{
  exception_<cException>("MyCustomException", PyExc_BaseException)
    .add_property("__repr__", &cException::message)
    .add_property("code", &cException::code)
    .def("some_additional_fancy_method", &cException::some_additional_fancy_method)
  ;
}

I have failed to implement this so far. Does anyone who is more familiar with boost::python know whether this can be realized at all or how?