I did a quick online search for high-res images of 1st and 2nd impression hobbit front boards, and it was inconclusive. If I had to hazard a guess, I would say that the stamping die was the same for the two impressions, but was not always pressed into the boards with the same pressure?
The casing design and discussion is covered in Hammond's Bibliography pp. 13-14. No mention is made of having to change it mid-print run, but it is interesting to read as it went through multiple revisions and options. A nice reproduction of the 2nd impression case is on p. 5 (no plate for the 1st impression case in the book, however.)