I've just encountered this and after banging my head against the desk for a few hours realised there's a step missing from the documentation.
In addition to the steps outlined you need to go in to IIS manager and to your WSUS site. Choose edit bindings and go to the HTTPS protocol (8531 if you're using the WSUS defaults, 443 if you're using the Default Web Site, doesn't matter). On here you need to choose which server certificate to associate with this port binding. Without choosing the server certificate SSL will simply not work, which is probably why you're able to connect to and administer the server over HTTP but not HTTPS.
It's one of those ones that someone who uses IIS all the time will do by second nature, but sysadmins who just use it for WSUS won't have considered.