A number years ago I went to my agent to do a visa run for my edu visa. I had 2 blank pages left so never thought anything of it, however he said I needed a minimum of 3 to do the run. I only had a few days left and my embassy said a new passport would take weeks. Immigration said they would allow me 11 days over and then I would have to turn myself in. I applied for a new passport and contacted every type of officials details I could find to get it sped up and luckily it arrived in time but I was in extreme panic mode.
You seem to be very sure an appointment is required as you've mentioned it twice now. Can you kindly show evidence that an appointment is required as I don't believe it is, since I will be applying for a SETV in PP and I was previously trying to gather feedback on the process.