this may be too crazy, but here goes:
Some engineering students receive a emblem called a "bent" that is meant to resemble a bridge truss. I remember it being sand cast in bronze, and you had to polish it. If you contact a university's Engineering College you could ask where they source them. Or you could contact Tau Beta Pi, the engineering society.

Not sure why you want sand cast - the finish is usually a bit coarse compared to lost wax. Some jewelers use lost wax.

Additive manufacturing ("3D printing") is another possibility using the sintered metal process. Others here have much more experience with it than I.

I would suggest you search past posts on 3 topics that are particular to the 55-56 V8 Packards:

1) Torsion-Level suspension

2) Their version of Ultramatic transmission

3) valve noise/oil pump

Mike Dulinski is a source for used parts for 55-56. Someone else here will have contact info.

That's a pneumatic window. :)

Flexible vinyl was invented in the late 1920's.

LaVine acquired the reproduction tooling and formulae from Yesterday's Radio when Jerry V retired. The quality is excellent, the parts are not cheap.
Your alternate, depending on how badly the old Tenite parts are (they were not really expected to last 80 years) is to fill with an epoxy or polyester then paint. If your car has one of the mottled, translucent look designs this is not an option.

quite stylish for its price when new

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Exactly. So calendared rubber sheet will be closest to this, but may bloom (exude a white haze). As far as using solvents, take great care - rubber compounds also use oils as plasticizers. With rubber (cross-linked) the failure mode is even uglier, a swollen gel.

I worked in automotive plastics, including formulating vinyl, and that article's distinction is complete BS. Vinyl resin (PVC) is rigid and rather intractable. You compound it with additives to alter its properties like ease of processing, weathering, coloring, impact resistance, fire resistance, etc. If you add a plasticizer to soften it, you get flexible vinyl, invented in the 1920's. The amount you put in (up to the resin's carrying capacity) adjusts its softness. "Leatherette" is just marketing speak for flexible vinyl or I suppose other flexible plastic.

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Wat, he is an absolute gentleman and has helped me with good advice and information several times. He's getting a bit older (as are we all) so have some patience.

Correct, sold to Carlyle (investment group) some time ago. Now called Axalta I believe