Here's my experience calling them from this morning. I applied end of April (application delivered May 2). New citizen/passport. Travel date June 24.
Started dialling at 8:30am, eventually got through to be on hold at about 9:10am. You just have to keep trying over and over. When you call it seems you either get through (you'll get a list of six options), a pre-recorded message that lasts about a minute (you can hang up as soon as you hear it), or just beeps as it fails to even connect.
When I got through there were 376 people in line ahead of me. You get an update every minute or so telling you how far the queue has progressed. It goes at about 30 people every 10 minutes (I made a note of the number/time every so often), so you can plan around that if you have other things to do. I got through after about 2 hours.
Agent answered and I explained I had upcoming travel (told them the date) and that I wanted to have my file transferred. They asked for my file number, which I did not yet have. Asked for the usual background information then put me on hold again while they reviewed the information. This second period of hold only took a couple minutes, and you got some different hold music to the stuff you'd been listening to for the previous two hours, so at least there's a bit of variety.
Agent came back and told me some information was missing from my guarantor. Unclear what information was missing, and I can't see anything on the form I missed, so not really sure why that would be the case. (Speculation: for brand new applications maybe they have to speak with the guarantor? Anyone have any insights on this?) They gave me a phone number for my guarantor to call to provide the missing information. I really hope for my guarantor's sake that they will not also have to spend hours on hold for this.
They were still able to request a transfer to my local office, although I assume my guarantor will need to call them before the local office will handle anything. They said it'd be $45 for express handling and "possibly some pick-up fees". They wanted to know the time of the flight, so have that on hand. They told me to expect a call from a blocked/private number either at the end of the week prior to my trip (so around June 17) or early the week of the trip. Usual spiel about no guarantees and that the local office may not even accept the transfer, etc. etc.
They didn't volunteer my file number, so I had to ask for it. I'd advise making a note to yourself to remember to ask for your file number if you don't already have it, in case you need it for a future call.
I made sure to explicitly clarify how the transfer process works given that they have my original citizenship certificate. They said it wasn't a problem and everything would be transferred over.
I didn't ask about what I'd need to bring to the local passport office (e.g., new forms, photos, etc.) - I figure I can ask the local office when they call me.
Now hoping my guarantor can get through to them quickly and then crossing fingers to hear back from the local office in a little over a week.