I'm quite sure you understand the existing procedure for expulsion or disqualification better than I do, so I'm not sure I can be terribly helpful on this question, but let me just react generally.
In principle, it doesn't seem to me that it needs to be an elaborate procedure that could lead to the judgment of the House or the Senate that a particular criminal conviction meets the threshold for triggering the loss of a pension. I'm not sure if the existing procedure is an elaborate one or not; I'm just not familiar with the details.
It would seem to me, for example, that a debate, an opportunity perhaps for the member whose conduct is being debated to contribute to that debate and have his or her views heard, leading to a motion and a vote on the issue, would be sufficient. I don't know how different that is from the existing process, but it seems to me that the important thing is to have an opportunity for debate, an opportunity for the member whose behaviour is at issue to contribute to that debate, and for a vote to be held after a full debate. That would seem to me to be a sufficient procedure.