Ok - so to rule out unknowns, I installed shib SP and am able to test the SAML flow with the Gluu installation and ensure I am working with the correct keys and certificates in the right places. https://gluu.org/docs/ce/integration/saml-sp/ was a great help to get this up relatively quickly.
We'll work through our webapp's SP implementation, I suspect there might be issues with it, even though we were using the correct metadata earlier.
Many thanks for your patience and assistance so far.