Using classic Outlook for Windows in business environments
No, webmail and Outlook don't have to match in their SMTP servers/ports. Either should work with Outlook, but webmail prefers the security protocol used by mail.centurylink.net port 465, i.e., SSL The SMTP server should not be involved in the problems you are experiencing.
I do see one strange thing that may be location dependent. If I try to do a reverse DNS lookup of the IPv4 address for 209.67.129.100 (mail.centurylink.net), it fails. A forward DNS lookup of mail.centurylink.net succeeds and says it is an alias for lumen.pangia.biz and its IPv4 address is 209.67.129.100. I don't know that Outlook should need to do a reverse lookup, but it is a bit strange to me. Note, this is still the case for me even though my IMAP connection is working now. However your DNS server may be different than mine. You can try it out using the "nslookup" command in a Windows cmd window or powershell.
Afterthought: Have you rebooted your Brightspeed modem since Oct 30th?