I was in process of writing a decent reply to that thread but as he had finished his case it seemed moot.
So here's my 2 Cents Worth!
I have some amateur experience with different types of foam through building props and costumes and the main factor in determining what to use, IMO, is the Resilience Factor. Most of the Expanding/Insulating/Packaging type foam is designed as either an expedient short term shipping solution or a low action insulation which will only see limited compression cycling. In other words, its like styrofoam, once you put a dent in it; it stays! And as a result, every bump will cause the foam to get larger very quickly and no longer hold the instrument tightly due to compression in all directions. Another consideration is that, except for Ultra Low Density Packing Foam, most are Very Stiff and will still transfer the shock from Bumps to all the Key Works.
Even the older, original case builders used upholstery foam rubber on top of the wood blocks and under the lining that have been the mainstay of sax cases for more than a Century to absorb shock.
A better choice, as can be seen in modern cases, is a moderately low density polyethylene with full resilience, in which when the weight of the object being supported generates a moment of movement against the foam (aka Bump), it will return to its original shape. The best example is the type of foam used in computer packaging.
The vendor I get my theatre foam from is a Hewlett Packard partner, so their density selection is usually pretty good and as I will need to build a case for my Evette when I get her rebuilt and already plan to get 2 different densities of foam. The outer shell will be a 3.0-4.0 pound density, which resists bending and can easily take a layer of Fiberglass OR a few coats of a Urethane Floor Paint or even be bonded to a laminate layer, and the inner, which will actually support the horn, will be a 1-1.3 pound which will absorb shock and minimize that transfer to the body of the horn.
That thread also mentions "Plucker Foam Boxes" and I've seen a few case makers out there using essentially that same method; making a straight outline cut of the horn and let the sides absorb the lateral impact shocks with seemingly no thought to "cradling" the upper tube and bell together. Also, as in the case of GigBags, there's not much else in the way of skin support.
Now one thought had come to mind when thinking of how difficult or easy to make the case. It might well be feasible to simply make a shell, use carved/fitted polyethylene blocks at the strategic support points down the upper tube, both bows and the bell, then use the expanding foam under the case liner where it would not only act as a filler but also as An Adhesive for the liner and the foam blocks! Just make sure to Saran Wrap the saxophone REALLY WELL as that stuff is vicious to get off Anything. Plus some of the products I've used lets off steam while it's expanding.
I may have to do this just so as to know I'm eating my own dog food.
If any are still awake out there you may now return to your regular channel. ^_^