I've dug through my library on campus and youtube, google, jstor. I keep finding books that quote him in context, or youtube clips, but I have not yet found a large compilation of his full speeches. Can anyone help me?
You mention the campus library, you asked your reference librarian? This is the sort of question we help you with.
I've seen some of his speeches in text format. However, they are on hateful websites due to Fr. Coughlin's anti-Semetic views. As such I will not link to them here. There are copies still around of Coughlin's collected radio broadcasts under the title Father Coughlin's Radio Discourses 1931-1932 (or something very similar, sometimes the formatting is different regarding the dates). I'd start with the book, and only after that think about how deep down the rabbit hole of hate-spewing websites you want to go.