I neglected to mention that there is a very viewable photo on Hillbilly Researcher's blog site of the 1946 Dixie Playboys. It was apparently published in a Glen Thompson songbook in that year and shows and names six musicians, but gives no certain means of matching names to men. With the UNC photos as a point of reference, you can probably get around that.
I found a list of 5 Glen Thompson/Nelson Teal 78s on Hillbilly Researcher's blog site. They were numbered 10-001, 10-002, 10-003, 10-005 and 10-006. He assumed the existence of 10-004 and left a blank for it. The first 4 listed discs had matrixes prefixed with NBT (for Nelson B. Teal). The first three discs had consecutive mxs from 101 through 106. 10-005 had NBT-111 and NBT-112. On 10-006, the NBT prefix was abandoned and a GT prefix (for Glen Thompson) was adopted. The number series was also switched and the two sides on 10-006 became GT-009 and GT-010. Now for the $64,000 question: Was 10-004 ever issued? UNC says there were 5 issued and we know about 5. If the GT series was counting issued matrices, it would reach #10 with the fifth disc. Mx NBT-112, however, admits of the possibility of 12 sides being cut, of which sides numbered NBT-107/GT-007 and NBT-108/GT-008 would have been available for issuance on 10-004.
Actually there is one photo on that site that I can see full-size via Google image search, and that is clearly showing that Babe Harrell was on string bass, Billy Purcell on steel guitar, Glenn Thompson on guitar (with his name on it), Sleepy Johnson on guitar as well (as we know, he also played fiddle and banjo) and Curly Gardner played electric guitar. There is also a fiddle player on this photo, named Rocky Stone.
So we can fix the release date as 1946: His band, the Blue Ridge Entertainers, performed daily on Burlington radio station WBBB; the band, with some personnel changes, changed its name in 1946 to Glenn Thompson and his Dixie Playboys. From that year to 1948, they released five 78s on Thompson's own label, recorded at the Nelson Teal Studios in Burlington.
There is also a photograph of the "Original Dixie Playboys lineup", showing Babe Harrell, Billy Purcell, Glenn Thompson, Sleepy Johnson and Curly Gardner. As I can't blow up the thumbnails there, I cannot say who played which instrument.
Sleepy is probably Sleepy Johnson, a long-time bandmate and usually a comedian in Thompson's associated stage shows. I don't know enough to guess who Curly might be. For someone in the vicinity of Chapel Hill, North Carolina, that answer and the accurate dating of all the Glen Thompson recordings in this series might be found in the Glenn Thompson collection in the University of North Carolina library system. The reference to Nelson Teal of Burlington, NC might be a clue to further resources and the reference to Radio Station WBBB in Burlington, NC might help nail down the date.