I have exactly the same problem.
I contacted Optus online chat support yesterday (just couldn't face calling them).
Apparently cable customer DON'T have the option to change their direct debit details in 'My Account', as they are on an old system and can't do this.The chat person told me (after a lot of unnecessary stuffing around as is normal with a chat service) you can either call customer service or send in a paper request which will take up to a month to process.
I just tried calling customer support (133937) and first of all got caught in an endless loop which offered to text me a link to a Web page that told me I could do what I already knew I couldn't do.
So I called agian on 133937 and picked an option that involved me buying something new and got a reply to a real person in seconds. She told me she'd put me through to "customer service" and they could help me but I got an answerphone telling me to call "during business hours" - but not what those business hours are.
I think I read somewhere on the maze they call a website that customer service closes 7PM, so I just missed them. Will try again tomorrow and let you know how I get on.
P.S. Roll on NBN - I'll end up with a cable service no better than what I have now (which will cost more too) but at least I won't have to deal with Optus "customer service" anymore.....
I did exactly what you said and went to technical issues and got redirected. Fortunately it was before 7.00pm.
Suggest they change the website but got nowhere with them understanding
Optus customer service is useless