Scott,
Your Dean photo is an original Burke. As for the "Type 1" designation, I've never been real comfortable with applying that to any Burke photo simply because of the 2-year window from when the photo was taken to when the print was produced that is part of the "Type 1" definition.
For example, the Dean photo would have been taken as early as 1934 (quick judgement based on his uniform, though other details may pinpoint that more accurately). So Burke could have produced that particular print in 1934, or 1935, or 1936, or 1937, or any year up through 1948 around which time he retired for health reasons. Only prints produced within those first 2 years would qualify as Type 1's, though any print that Burke produced (signified by his stamping on the back) would be considered an "original" (i.e. produced by Burke's hand from his original negative).
With Burke photos, the stamping on the back is the important factor in determining an original from a later-era print produced by George Brace, Jim Rowe, or others. If it has "Geo. Burke 847 Belmont Chicago" it's an original, produced by Burke sometime between when the photo was taken and 1948.
Also, others have mentioned the typed coding that often (but not always) appears in the corner of Burke's original prints. The first number represents the player depicted. The second code typically starts with an N or A (for National League or American League) followed by a number which signified the team represented. If Scott scratched around under the paper affixed to the rear of his Dean photo, for example, if the code is there, I would expect it to be "187 N8" for Paul Dean in a St. Louis Cardinals uniform (fwiw, Dizzy was #186). The code is not "shot-specific" by which I mean that the same "187 N8" could appear on any photo of Paul Dean in a Cardinals uniform, of which there are at least several that I have seen. It does not refer to a specific negative, but rather a specific player/team combination for which there could be a number of different poses which may or may not have been taken on the same day. Flipping through a few other photos I have here, I see that he also used "U-#" to refer to umpires, as well as "T-#", "C.P." and "W.F." to refer to other executives, though I haven't yet given thought to what those codes would represent.
Another example of a Paul Dean by Burke, this an 8x10:
