Think outside the box.
Now, I don't know the Athens area at all. But here's a technique that I'd use around here, and it should work in Athens as well.
Market directly to owners of 1950s brick ranches. Don't worry if they're on the MLS or not. It doesn't matter. You may be right that some sellers have pulled their houses off the market. Others have never put them on; they figure they won't get any offers, so why bother. Your Realtor can pull up listings of all 1950s ranches, and get the contact information for the owners.
Your general pitch (or that of your Realtor) should be: "Hi. I'm interested in buying a 1950s brick rancher in Athens, and I understand you own one. I'm willing to buy it in "as is" condition. I don't mind if it has the original kitchen and baths, or whether it needs repainting. If you'd consider selling me your property, please call me at xxx/xxx-xxxx." You can smooth that out and build on that, but that's the basic message.
There are two sub-markets you especially should target. One is absentee owners. I don't know whether properties you're looking for are likely to be rentals or owner-occupied. But have your Realtor do the same search, but limit it to non-owner-occupied properties. Your pitch should be something like: "Hi. I understand that you own a 1950s rancher in Athens, and that its currently being rented out. I know that renting can come with headaches--finding new tenants, dealing with repairs, waiting for rent checks. If you'd like to end those headaches, I may be able to help. I'm interested in buying a property like yours. I'm willing to buy in "as is" condition........" and so on.
The other group to target are people who've lived in those houses for a long time...or perhaps their relatives or children. Up in Northern Virginia, communities like that have a lot of older residents who are unable to maintain those homes, and are moving in with their children, or into assisted living or nursing facilities. Or, sometimes they've died and their children are interested in selling. Your agent will be able to screen the MLS for properties in which the last sale occurred, say, more than 20 years ago. Then contact the person the tax notices are mailed to; your Realtor knows how to do that.
And a bonus tip: To reach the older people, or their relatives, contact attorneys who specialize in wills, trusts, and estate planning. That probably will take more than just a letter, though you can start with a letter. Your pitch should be along the lines of: "Hello. I understand that, from time to time, you are aware of properties that are subject to estate sales, or properties that the relatives of the owner are trying to dispose of. I am interested in buying such a property--specifically, a 1950s brick ranch. If you are aware of any such properties that someone would like to sell, I would be very interested in them." And so on.
There are a lot of other creative techniques to find such properties. But those should get you started.
Hope that helps.