I happened to have some new, never loaded or fired Starline brass in .38 Special. Keeping in mind this brass is already sized to be loaded, I found a 0.355" pin gauge was about as large as could slide in with some friction, but it stopped rather abruptly at a distance of -0.640" in past the mouth, so that's where the taper to the head area gets thick in it. On Ed's recommendation, I bought a couple thousand of the Remington wadcutter bullets the last time they were available on Midway, and they measure 0.630" in length. So they should do very nicely using the Starline brass as wadcutter brass for them and experience no reverse tapering of the hollow base skirt in the case.
RMcL,
I don't have an answer to your question regarding which dates and loads were involved. I'm not a cartridge collector, so I am having to go on photos and memory of examples I've seen in the past. The cannelures used as an ID code is interesting and I am thinking of calling and talking to someone who makes revolver cartridges with cannelures to learn exactly what they do or don't mean today. I have seen cannelures in .357 Mag brass gradually iron out with repeated loading and firing, so they must have enjoyed some degree of indentation "below grade" originally. But they can't hold a candle to the depths of the ring grooves that used to be formed by manufacturers, so I expect the purpose has changed over time.