Remember that nobody ever said "Gee, what a convenience this voice menu was for me"
But that does not mean it was the wrong option...it just means that menu = customer must live with less than they hoped for.
Another philosophical point to ponder is the option of simply returning a busy signal. Your end users expectation or assumption may be that busy sig means “your busy” or it may mean “Call the CIO and ask what the shuck is wrong with the system” Consider that a busy is far better than ring-no-answer and far better than a bad voice menu.
To proceed with the menu idea, what I do in my department after 8 rings is play a message like 1) to continue ringing, or 2)to report a problem [rings the real Help Desk]
In your case, you are probably the last place to call with no alternatives/backups. That leaves you with few choices: Continue, or Leave Message.
If 4357 gets lots of calls that should go to another area, the menu could offer those suggestions/menu choices. But test this: Create a menu with #1 going to a phone that is forwarded to voice mail, and #2 going to a phone that returns a standard busy signal…call and ‘listen to the love’…the way MerMail sounds in those cases is very customer unfriendly.
I know…this is an answer to a question you didn’t ask…but, someone will read it and get tears in their eyes…