Just to confirm, your application is the IdP and when the SAML response is sent to the partner SP's assertion consumer service this results in a 404?
Are you using the SAML middleware or calling the SAML API?
I'm not sure exactly how the IAuthenticationSchemeProvider is impacting SAML SSO but the two should be able to co-exist.
Are you able to reproduce the issue with the ExampleIdentityProvider and a test IAuthenticationSchemeProvider implementation?
If so, please zip up the source code and send it to firstname.lastname@example.org
so we can reproduce the issue and investigate further.