Ah, that makes more sense. 1/4" is substantial, but the thickness I suppose doesn't bother me that much other than vintage correctness, so maybe it'll get shaved down one day and maybe it won't. I took out the tape measure and compared it to this picture (below), and everything lines up pretty closely on the BaCH. I will likely need to get a different pickguard as the current one sits a little high on the body so it's closer to the edges than a Gibson, and my OCD is kicking in on that.
@TBird1958 what did you use to black out the headstock on the Cherry one you had? I'd like to do the same before it gets a full refin down the line.