I just phoned Telkom sales again, and used the option to track status of my order. The lady actually had some new information: she said that CW has finally released the lines now and that I have an option: I can either stay with them, move to a different ISP, or move to Telkom. I told her I want to move the ADSL line portion to Telkom. She then said she can see my pending order, but that she can now actually confirm it (which they couldn't/wouldn't do this morning when I asked for it) after which it should take 12-24 hours.
So now we wait, but at least she did say "No, it's definitely not 7-14-30 days or anything like that, and we know a technician doesn't have to come out to you, it's all automated from here on.". Sounds like I'm not her first CW customer for the day, heh.
She was actually pretty cool about it. Even laughed when my response to her question: "do you want to keep the line with CW" was "HELL no".