JAX-RS and EJB exception handling

I'm having trouble handling exceptions in my RESTful service:

@Path("/blah")
@Stateless
public class BlahResource {
    @EJB BlahService blahService;

    @GET
    public Response getBlah() {
        try {
            Blah blah = blahService.getBlah();
            SomeUtil.doSomething();
            return blah;
        } catch (Exception e) {
            throw new RestException(e.getMessage(), "unknown reason", Response.Status.INTERNAL_SERVER_ERROR);
        }
    }
}

RestException is a mapped exception:

public class RestException extends RuntimeException {
    private static final long serialVersionUID = 1L;
    private String reason;
    private Status status;

    public RestException(String message, String reason, Status status) {
        super(message);
        this.reason = reason;
        this.status = status;
    }
}

And here is the exception mapper for RestException:

@Provider
public class RestExceptionMapper implements ExceptionMapper<RestException> {

    public Response toResponse(RestException e) {
        return Response.status(e.getStatus())
            .entity(getExceptionString(e.getMessage(), e.getReason()))
            .type("application/json")
            .build();
    }

    public String getExceptionString(String message, String reason) {
        JSONObject json = new JSONObject();
        try {
            json.put("error", message);
            json.put("reason", reason);
        } catch (JSONException je) {}
        return json.toString();
    }

}

Now, it is important for me to provide both a response code AND some response text to the end user. However, when a RestException is thrown, this causes an EJBException (with message "EJB threw an unexpected (non-declared) exception...") to be thrown as well, and the servlet only returns the response code to the client (and not the response text that I set in RestException).

This works flawlessly when my RESTful resource isn't an EJB... any ideas? I've been working on this for hours and I'm all out of ideas.

Thanks!