After hours fiddling with this, I post the question, then find a fix!

I had to SSH in to the box and edit extension.ini to add extension = php_openssl.so

After re-uploading that, it gave me the option in:

Web Station > Script Language Settings > [profile] > Edit > Extensions > openssl

I swear the option was there and was ticked before, but was now unticked. Reselected, saved, and it works....