Oh, this is terrible. I sympathize! I too had an Avios booking that for some reason couldn’t be changed online. Normally I am able to rebook or cancel Avios bookings but this one required a phone call. I kept putting it off and fortunately (!) they cancelled the flight and offered me a refund. Now I’m hesitant to make new Avios bookings as the wait times seem horrendous. In the past I’ve had luck with the chat so that might work. They typically ask for a phone number in case you get cut off. Alternatively, you can just volunteer the phone number/e-mail, booking reference and what you need done right away in one of the first messages and tell them to go ahead and email a confirmation to the address on file.