The documentation is correct. We only support 443 for SSL. Sorry.
Maybe the option is not supported. But if you stop the IIS service and other services using port 443 (Reporting Services in our configuration). Edit HTTD.conf file in the Tableauserver/data/tabsvc/config directory and change port 443 to 444 for the 3 references. Tableau server will only check if port 443 is in use when starting up so start Tableau server first then IIS and other services using port 443 and it will work. Tableau server SSL on another port then 443.
See the trusted ticked response from Tableau Server using SSL over port 444:
Don't forget to open inbound TCP over port 444 in the firewall.
Hope this helps.