Durometers and equivalent Shore Hardness

A cobbler friend, and many others I suppose, use a press to complete bond of soles with commercial rubber-cement like adhesive.
His works up-acting, ram carrying the shoe forms. Above, foam rubber blocks distribute pressure evenly. Pic not identical, but similar operation.Attachment 19443 There is no heat involved, and blocks are mounted to 11 lamination plywood. His blocks are severely worn, and asked what could be done about replacement. Company built the machine offer replacements at a staggering price. The rectangular blocks are 110mm x 270mm x 100mm, and as mentioned resilient foam, with a structure about like Styrofoam cells.

I don't have or know anyone with a durometer. Has anyone an alternate method, to pursue material performing at least something like original?
No, haven't found a supplier in the immediate vicinity, who should be able to squeeze it and say "...that's about xxxx Shore...", figuring I''ll end up on the 'net and order. It seems logical to make a couple sets. Hope is for bulk material and bandsaw into size.

https://en.wikipedia.org/wiki/Shore_durometer Durometers, measure in one of a set range: Types A, B, C, D, DO, E, O, OO, OOO

Can't figure how to term specialized topic into a 25 character tag...rubber measurement technique, comparator, rubber hardness scale.

Not sure of exactly what you need but running shoe soles fall in the 70a range while fire-mans boots will have soles around 80a the density of any pressing block would need to be harder than the soles being bonded probably nearing 90 a to 100a Think of th ehardness of the average shopping cart tire as 100a
I am thinking that replacement blocks could be made from poly urethane the same type as one would cut hydraulic cylinder seals out of the chart below may help
Attachment 19444

Sellers of "O" rings should have a Durometer tester. If you take in an unknown specification "O" ring, they can quickly test it for you to determine how hard it is.
Or alternatively contact the original manufacturer and ask them what the Shore hardness is.
The problem then becomes one of buying a suitable product for your press where the seller knows the rating of what is being sold.

Perhaps you are making this more complicated than it need to be. It sounds like a simple press that presses the soles onto shoes, how hard can that be. Sounds like it is just a big clamp with a jaw that molds to any shaped sole to clamp with even pressure. If it has a structure like styrofoam you could try closed cell foam like is used in hikers sleeping mats. Usually about 1/2" thick and they are very cheap, give one a poke with your finger and see how it compares. If not thick enough glue it together in layers with the shoe glue. Knife sheath makers use similar foam to hot press Kydex sheaths into shape which is a more complex shape than a shoe sole, and it works very well. I would consider covering whatever you make with some sort on non stick covering to stop any shoe glue contamination if this has been a past problem. Perhaps a silicone baking sheet of some sort would work.

I am pleased to read that real shoemakers still exist. Around here they have all but disappeared with the onset of our throw away society. I don't know of anywhere that they would be capable of putting a new sole on a shoe, not even the cheap stick on soles that people once put on new shoes to make them last longer, (if you could still buy them).
If the band-saw doesn't work, try an electric carving/bread knife or perhaps a hot wire cutter. I saw a rubber retailer using the electric knife years ago and it worked well with nice clean edges.

I don't have much experience with anything but sheet rubber gasketing, virtual babe in the woods with this project. Sleeping mats! Ideal hint, and the more closed cells won't abrade anything like originals. Laminating will be easy, along with trimming, have a wavy edge saw band. I'll laminate two full pads layer by layer for 70mm [ish] thickness, probably wind up with 4-5 pair. I started with the OEM on density; they're no so inclined to oblige. lol TM51 plays hmt.net trump card.

When (actually before) I started working it was impressed upon me "Nothing on a shoe can't be replaced." Time and and shift from general industrialization dilute simple truth. It still holds, with the rejoinder "...if initially made properly."
Here in the Midwest there are few shoemakers; shoe repair/ cobblers (what they'll undertake) is somewhat more prevalent. I've noticed that shoemakers occur in two places and serve two variety of clients. One are [rare] solid middle class blue collar areas as many occupations are dependent on their feet. They will spend money on correctly built Goodyear welts and occasional Blake stitched. Either way, it is surprising that trades unrelated to 'handwork' know to shun adhesive construction. Cheap shoes are cheap all the way through. The significant costs are defrayed by re-sole/ heeling on worn-in [comfortable] uppers. Many will get 3 go-rounds on the same pair.
Serving other client base occurs in the most distinctive neighborhoods, making fully custom shoes to order. Won't find so many examples of heavier duty footwear, or customers there.
I was unable to acquire service at just such a place, they were aware of just not tuned to that market. At least they provided a valuable referral. Thanks so many reasonable shipping companies and social media exists, versus isolation or inhabiting wrong end of market, there is a solution. Blatant plug? yup. Satisfied? time and time again. Geno's Shoe Service, 1164 W 103rd St, Kansas City, MO 64114 Ph. (816) 765-7463