Sir:
Good luck with that. I found a girls class ring 2 years ago and it has become a chore to find the rightful owner. It had 3 initials inside. I've determined from the internet that there were 7 girls with those initials in that class. I've managed to contact 3 of the seven. All had lost their rings and thought it was theirs. However, they didn't lose it where I found it!
A guy's ring should be easier because he didn't change his name if he got married. Did you Google Scott D. May? If you did and came up empty, try looking up that class's reunion on the internet. You may find other classmate's email addresses. Email them all and ask if they know where you can find him and be sure to tell them why. People are very spooked by strangers emailing them.
Good luck!