An excellent question, but unfortunately not one that I have a complete answer for. In his American Record Label Book, Rust states that American Brunswicks from the end of 1923 through the beginning of the ARC period in January, 1932 do not show the mx numbers in the wax, although some earlier issues of that time frame do show the last two or three digits in miniscule type near the rim of the label. The Brunswick ledgers still exist, although incomplete and hard to get access to at the MCA offices. Also, English Brunswick Cliftophone issues of American recordings between 1924 and 1927 frequently do have legible matrix numbers in the wax or under the label. So there are several ways that at least some issued mx numbers might be discovered, but probably no way to be sure that we know all of them, which is probably why the ODP retains the full range of mx numbers in the "control" column. Access to the original masters, if they still exist, might possibly allow aural identification of the takes used by the minor differences that must exist between them and their presence or absence on the issued discs. Auditing a sufficiently large sample of any given title might help determine how many takes are represented, but give no clue as to which ones they are.
This is very interesting information. Now I wonder how Ty Settlemeier or Steve Abrams manage to identify which of the matrix numbers that Brian Rust found listed in Brunswick's archives was actually released? Is there anything on the records themselves that allows us to identify the matrix/take used? I noted down everything I found stamped into the runout of my copy, but am not sure what these number and letter combinations mean. They are clearly not identical with the take numbers.
Brunswick in the 1920s did not use a matrix number with associated take number system like most labels. They gave a separate master number to each take. The takes were usually recorded and numbered sequentially. Thus when you see a listing in Rust's books for a Brunswick recording of that period you will typically see the first number in the sequence, followed by a slash and the last digit of the last number, indicating that all the numbers in between are takes of the listed title. If you go to the source indicated (The Online Discographic Project, as it happens) you will see that they have done the same thing in the column labeled "control", the apparent source of BigBadBluesMan's numbers. The numbers there are identical to Rust's from the American Dance Band Discography, which suggest that Rust either did not know which mxs had been issued, or possibly thought that all of them had been. In the ODP's column labeled "matrix", however, you will see the number 12381 for side A and 12383=4 for side B, indicating that Ty Settlemeier or Steve Abrams have decided that those are the mxs that they know or believe to have been issued.