I was wrong when I said we had gone back and disabled all comments and trackbacks for previous posts. As it turns out, we did not. The comment from Dan above made me realize our error as when I began to scan our logs, I noticed these were all previously published pages. Whomp, whomp.
Our solution was to run the following two SQL statements on our database to shut off comments:
UPDATE wp_posts SET comment_status="closed";
and pings:
UPDATE wp_posts SET ping_status="closed";
for our previously published posts.