I believe he immmediately went on a tour of Georgia once accepting the UGA job to promote the school and recruit students and became ill during those travels before coming back to Athens.  If you have not done so already, check out History of the University of Georgia by Thomas Walter Reed; Frontmatter and Chapter I: The Beginnings of the University, Thomas Walter Reed,  Imprint:  Athens, Georgia  University of Georgia, ca. 1949. It states he took part in the commencement in the spring and then started his PR tour.  That source also indicates that the UGA Board of Trustees was actively recruiting Finley for the job.