OK, there's not as much difference as I thought.
My Gretsch 5123 body is 2 3/4" front to back. My old Univox 335-copy is only 1 7/8" front to back, so no wonder there's a very perceptible difference between them...but I can't think that 1/4" would make much diff between the 5123 and the Broadkaster.
I don't remember the dimensions of the Casady bass I had, but I think it was about 2" to 2 1/4" front to back.