I don't know who Barton was or why he or she was special but I sure wish I did. I have a 1934 dated catalog that doesn't have the Barton's Special holster in it, my next closest catalog is from 1940 and it does show the Barton holster as well as the Threepersons holster with an "extended hammer cover".
Here's page number thirteen from the 1940 catalog.
There was at least one Texas Ranger named Barton and an Arizona saloon owner and gunfighter named Barton but I've never been able to come up with the Barton associated with the holster.
The first catalog showing the dog ear style is an early post WW II catalog, undated but I believe from the late 1940's. Both styles of hammer protector are shown in this catalog.The next dated catalog that I have is from August 1950.
Regards,
turnerriver