An old question Til, but my two cents, as this is exactly what I'm trying to do with my Schweitzer ancestors. It is perhaps feasible, but it is a great amount of time investment, and it depends on whether neighboring records exist, and how common the name was in that area.
In my case, the earliest actual record is his marriage in Weiterode in 1696, but town records go back several more decades, so I know he wasn't from that town. I'm mapping out and saving a copy of every instance I can find of either Schweitzer or Schnitzer in the area, pre-1700, to try and get more information. Nearly all towns have records to the 1670s, and many go back at least a few more decades than that.
My work is at https://www.google.com/maps/d/u/0/edit?mid=1_cHy99goGI3DEpQ_6ma9HSY9CxEXQ26H&usp=sharing
* Blue = I've not looked yet
* Black = no record of Schweitzers/Schnitzers
* Brown = no records exist pre-1700
* Pink = No Schweitzer or Schnitzers, but Schwätzers found
* Orange = these are so I can keep my bearings on the map;
I have other known ancestors from these cities.
* default pin = I've not looked up that city for DNA matches yet
* large circle with dot in center = no DNA matches
* tiny dot = no DNA matches
* star = A DNA match has a pre-1750s ancestor from this town
All DNA matches are autosomal; I have exactly zero y-DNA matches. And I'm always keeping in mind that just because the DNA matching person has an ancestor from there, I myself may not share that ancestor, or even that line at all.
I don't know that Schweitzers and Schnitzers have anything to do with each other, but I'm tracking both just in case. The majority of the green dots are Schnitzers.
Oetmannshausen seems a really good possibility to be the place I'm looking for, but it has one issue that the others don't. Namely, the 1651-1850s church book is not available on archion.de or elsewhere online. I am currently talking with the Kassel archives to try and obtain a copy, as an older scan of it does exist there on microfische. Someone online did have a professional genealogist look at those same fische 12 years ago, and found record of a Schweitzer family living there, with a Schweitzer-Krug marriage there in 1715. I have no known Krug ancestors, but it seems that quite a few people from Oetmannshausen and Rechtebach emmigrated together to the US in the early 1700s. Digging further, I've found quite a few Dilling, Beck, and Krug DNA matches for Oetmannshausen, and the same for Funk and Santrog from Rechtebach, so it looks quite possible... if I can get a copy of that particular church book! :D
Some things that might be helpful if anyone else is trying to do this in this specific area:
You also will have more difficulty doing this for your Thuringian ancestor. The church books exist, but the Alterstedt area records still all only exist on films. Personally, I'm still waiting for the Treffurt, Schnellmannshausen, and Falken records. They should all go up on archion.de someday, but there is no eta, and it could be years still before those records are made available online. I have a map of what records are available in this area on archion.de at https://www.google.com/maps/d/u/0/edit?mid=1_pxDZIro-69H0SYhlSh4AYmjz9rdVTEt&usp=sharing . The Landeskircheliches Archiv Kassel has been really good about getting books to archion.de over the past several years, but the books you'd need are the black dots, from the Landeskircheliches Archiv Muhlhausen, and they've gotten none of the books from that area to Archion yet.