Your system involves an open vote tally. I just went to Wikipedia. There's a Wikipedia article on everything, including separate articles on each of the two House of Lords Speaker elections. In Canada we've always kept our results confidential. My proposal would continue to keep the results confidential, and in fact it tries to put an extra measure in to make it harder to see when people are eliminated with essentially no support at all, in order to avoid any embarrassment to them, but I'm not sure that's necessarily the right way to do things. I'm simply following through on the spirit of what we already had.
What is your view on using the open model you have versus keeping the results confidential and known only to the clerks?