The January-February 2021 issue of Scottish Rite Journal, a magazine devoted to Freemasonry, has a cover story about Houdini's involvement with the Order. "The Sorcerer's Entered Apprentice" is written by Maynard Edwards and is well researched.
I'm not sure where one gets Scottish Rite Journal, but you can read the issue in full at the Scottish Rite website. Just keep it secret!
UPDATE: The author of this article has provided a revised and updated version as a Guest Blog HERE.