Thanks for the feedback and suggestions, guys. I'm increasingly happy with where this is headed.
To improve the nozzle, I increased the taper angle to to 78 degrees, lengthened the nozzle a bit, increased the diameter towards the tip, and increased the edge radius at the tip a bit.
I also increased the vial chamber diameter by a tad, which now makes the wall thickness look better.
Here are some of the latest captures:
Here is a wireframe of the model, oriented in a similar way to the auction photo:
That then inverted, overlaid at 50% opacity over that photo, rotated a bit, and scaled to match the tube diameter:
The contours seem to match pretty well. There is more finessing to be done, but I think it's headed in the right direction.
Something also still seems every so slightly off to me about the tip. Maybe the angle is still a little off?
Here is 78 degrees, which is what looks best when lined up with the auction photo at an angle
Here is 77
Here is 76