Because of certain elements in the story, I was able to narrow the date down to 1943 - 1947. I was unable to find weather records of this period and without a specific date, it was very difficult to search newspapers.
Yesterday though, things fell together. I saw a tweet from geneabloggers about a website called GenDisasters. I searched their database for tornadoes in Georgia and this article caught my eye. The tornado discussed in the article was within the correct time frame and just a short distance away from the area I was looking at.
Now that I had a possible date, I went to newspaperarchive.com, where I have a subscription, and searched for "tornado" in April of 1944 in South Carolina (their GA newspaper collection is pathetic but luckily my ancestors lived on the border). Very quickly I found an article that correlated to the one from GenDisasters. But, was this the tornado I was looking for?
Yes, it was! The article listed the areas hit, which included Elberton, GA (!) and the people who were hospitalized in the aftermath. Included as 17 year old Augustus Seawright, who I assume is the 17 year-old Seawright boy from the story.
Success! Happy Dance ensues.
Here are the newspapers (click for larger image):