Many thanks to the remarkably helpful staff at Tulane Special Collections! They provided more clues that will allow me to once again pick up the search for Mallord.
Susanna Powers reminded me that Mallord published two books, a fact that I had filed away during my last search. Today my copy of Moving Against Quiet arrived in the mail. It was published eleven months after Love Alone Finds Cold. On the back cover there is a picture of Mallord (sans beard), which graces this post.
The content of the book is similar to Love Alone Finds Cold, a blend of psychedelic writings and Romantic posturing with echoes of the beat generation. It is worlds away from Toole's literary forte of acerbic wit. But somehow these two writers connected, if only for a brief moment, just before Toole's final journey.