From what I see, I don't understand why they didn't just go ahead and make the tenon push type out of vulcanite in the first place then.
They did make the tenon out of vulcanite. That's what I'm showing in the picture - a vulcanite tenon attached to an amber stem.
Unless they were just trying to give the stem that amber look, in which case, vulcanite would be out the window as far as aesthetics are concerned.
Amber stems were very much the rage at the time these pipes were made. And we're not talking about amberoid or some synthetic version. That was largely used for the cheap crap. We're talking about actual real amber. But the amber that was used was, unlike a lot of amber, quite brittle and subject to chipping or breaking if not handled with care. So the folks at Barling were trying to come up with a way to use the best material for the specific function. In this instance, using a vulcanite tenon, which has more flex and give, to make the tenon, which has to handle shearing forces against the inside of the mortise as well as providing a more durable attachment than bone connectors of the era provided.
Looks to me like they could have just seated the vulcanite tenon portion up inside the amber and secured it that way, but I see how they could have even tried that method and decided threading it in made for a better connection.
Correct. That's what they did. The vulcanite tenon cap also provides a shield against shearing forces torquing the connector, when butted up against the face of the amber stem. Countersinking the tenon into the amber stem would have exposed a larger face of the amber to the shearing forces. Yep, no engineering in making pipes...
Just so hard to know what their methodology was back then since it's not like they all kept the most meticulous records of everything they tried that didn't work.
We don't know much because the records were largely destroyed. But they, and others, clearly had a methodology for achieving what they wanted, one that could be passed on. We do know that Barling were always looking for better designs as evidenced by the surviving patents for various bit, filter, and system designs that were, or weren't, actually put into production. They were inventive little buggers.