Thanks for the reply.
Yeah I understand its hard to suggest something else for me to check, it really does seem like a misconfiguration.
I ran both configurations through a diff-ing tool, doesn't appear to be anything unusual like trailing whitespace, improper indentation or extra slashes. From what I can tell they still appear to be equivalent configurations between deployments.
I tried removing the xpack.security.public segment of the Kibana configuration. The already working configuration continued to function, the non-working configuration is still running into the same issue. This makes configuration simpler though, which is nice!
I also captured the SAML response headed to each deployment and diff-ed those as well, they only appear to differ in the places you'd expect (audience, destination, etc). Both of those fields have the same format in both SAML responses.