This listing is new as I changed the old one to the Eldorado because I had the 2 mixed up. What I was listing as the May at 111 W. State was incorrect. Based on a 2009 submission from someone in the area, they indicated the building that housed the May was across the street from Gold and Sons. Gold and Sons was at 138 W. State at that time as far as I can tell. Their old building seems to be gone.
Using that information, I am surmising the May was at 137 W. State which still stands. It is an empty building that has been used for many businesses over the years. It was built in 1900. The frames on either side of the door of this building look like movie poster size. Another submitter said it was the home of an HVAC supply outlet but that has since moved or gone under. I am posting a photo of that building until I can nail this down for sure.
I did find some minor mentions of the theater in the news archives. A July 1959 issue of Box Office Magazine had this mention: "Douglas Moore has closed the May at Montrose." I am not sure if the theater closed for good in 1959 or if the Box Office article was mentioning this as a seasonal close. Oddly, some theaters closed during the summer back then. Whether they had A/C or not was probably a factor.
UPDATE - My theory is confirmed by the Facebook posts shown below. Local residents weigh in.