That output is really helpful. The plugin is certainly working as you would expect. It's connecting then following the redirect, but it's that last connection that is stalling. It's timing out before any HTTP status code is returned.
If you would like to increase the timeout beyond 60 seconds, then there is a global setting in the main Nagios configuration file that will need to be adjusted. Generally speaking, it's good to maintain limits here in case there is a runway process that needs to be terminated. I would try to increase this to 120, and test once more.
Hmmm... if the website is loading but check_http is timing out, this is a puzzler. I don't believe the plugin is failing as it's able to connect initially but is timing out on the redirect pages.
Let's move this one over to a support ticket, so we have the option to set up a session if necessary to troubleshoot further. Thank you for your patience.