Make sure you have put the SAML startup microflow in your application's After Startup microflow - without this, SAML won't work. Your DefaultLoginPage should point to a login page, not your index page - this could be login.html. The SSOLandingPage looks correct. You shouldn't need to edit the login-with-sso.html page at all, as this should only be used when trying to login using the Mendix provided SSO, with your Mendix account.
As long as you have the redirect on your index.html page setup properly (which it appears you do) and the SAML Startup microflow in your after startup microflow, you should be redirected to your configured idP for SAML authentication.