So I called them, and changed it over. I also removed Telstra Home Messages 101 (some crappy voicemail they offer) and calling number display (as it doesn't work with our phone). The girl seemed competent enough and I was happy.
A month later, we get our phone bill. We have been charged for 2 days of Homeline Budget, then a month and a half of Homeline Plus. Irritated, I call Telstra and ask why I've been put back on Homeline Plus. The guy tells me it must be a "system error" and he'll change it back. Just a little interjection: I worked at Telstra for almost a year, and I'm pretty sure I know how it happened, and it wasn't system error. Still, I don't say anything and he credits me the half-month of Homeline Plus, and tells me the rest will be credited on my next bill. So we pay the difference and wait.
Fast-forward another month on, to today. We get our phone bill, and lo and behold, there's no mention of Homeline Budget at all, just Homeline Plus. Also, there is no credit for the previous month. So, I call Telstra again and speak to Michael. I tell him the saga and he says he'll change me to Homeline Budget again. Trying not to sound irritated, I ask him if it will stay that way this time. He admits the previous consultant either "didn't do it for some reason" or "did it wrong". Great. So he changes it back and credits me 1 month of Homeline Plus. I ask him what happened to the other credit the guy was meant to put on this bill, and he says I don't get that and he "already credited me too much" because I should only get the difference between Homeline Plus and Budget for those months.
Now, I understand that. But I would think that after attempting to change this thing 3 times, I deserve a free month or something. Christ, when I worked there it was almost standard to do that. But whatever, I thanked him and hung up. We'll see what happens next month.
tl;dr - Telstra are Evil Overlords and I wish there was some other phone provider to go with in Australia that didn't involve renting the line from them.