I once wondered how skate boot outsoles were made. Most leather boots use "hardened leather" soles. I assume you could make a shim the same way.
A very quick, non-authoritative web search shows that there are actually many ways to harden leather - though at least one of them said some of them work better with some types of leather than others.
Nonetheless, it seems like leather is actually pretty easy to harden. Not just adhesives (some say epoxy works well, others disagree), but also hammering, and baking, which at least sounds ridiculously easy. People used to make leather armour (and hobbiests still do), that was very durable.
E.g.,
https://mazeleather.com/4-ways-to-harden-leather/https://www.youtube.com/watch?v=hwGW_qwpxYshttps://hackaday.com/2019/05/26/loads-of-testing-yields-new-reliable-and-cheap-leather-hardening-technique/https://medium.com/@jasontimmermans/a-comparative-study-of-leather-hardening-techniques-16-methods-tested-and-novel-approaches-8574e571f619(I'm just listing the first few entries from a Google search on hardening leather. I'm sure you can find many others.)
It sounds like some of these methods would be pretty easy, fast and rather fun to try. Furthermore, if you weren't happy with the results, you might be able to remove the leather shim you produced. Though if you used an adhesive while molding the shim to the boot, you might have to sand it off - but I'm sure you have the tools to sand things.
All of these methods have an obvious problem. People love Edea boots partly because they are fairly light. Shims add weight. I'm not sure if the shim you are talking about is large enough to worry about the weight. But if it is, how would you find a lightweight but relatively uncompressible and durable shim. That sounds like a materials science or engineering problem - and I guess you have the right background for that.
I suspect wood is one of the lightest materials you could use. In the boating world, West Systems Epoxy, possibly the biggest marine epoxy supplier, advocates infusing wood with one of their epoxies, and that can last a lot longer than most skate boots last. But that would add a fair bit of weight. Bill_S has mentioned using Silicone to waterproof boot soles - though I don't know how durable it is.
I've become interested in building my own lightweight sea kayak. A lot of people use wood (both natural wood and plywood), because it is light and easy to work, though it needs to be waterproofed and requires some care. People on boatdesign.net, which has a lot of engineers, say it also has a relatively high strength to weight ratio, and tends to resist crack formation, so it doesn't break as easily under long term stress as some materials. Many skate boot makers have already used wooden heels - I assume for the same reasons. The ease with which wood can be shaped might make it fun to play with too. Sometimes people infuse it with steam, or use "live wood", to make it more flexible, to comform to shape, perhaps like the bottom of the Edae boot. Sometimes they laminate several layers of thin wood instead to comform to shape.
(BTW, someone in this discussion wished coplanar boots and blades were available. For blades, they could look at
Goldquest coplanar blades, which are still available, as of a few months ago. They also have separate adjustable toepick heights and styles, so the blades can be used longer. On traditional skate boots, with thick leather soles, people sand the outsole to be coplanar too. Unfortunately, with the very thin outsoles on Edea boots, you obviously can't sand the outsoles to be coplanar, plus you already have the blades, so it's completely irrelevant to your case.)