I looked up Alpha Delta in Baird's and there isn't anything. I also looked up the list of colleges and universities where fraternities and sororities were founded and there are only two listed for Monmouth - Kappa and Pi Phi.
There is an Alpha Delta listed as a journalistic recognition society but it was in Illinois in 1929.
Loved reading the story. The Kappa key is one of my favorite badges, bar none.