So sorry to hear you haven’t managed to speak to them, I know how stressful it is. This system sucks.
I have not heard anything other than an automated email from the upgrade team saying they have noted my travel date. No idea if it will work. Have they confirmed you can’t upgrade if it is a first passport?
In my experience it has taken about 4-5 days to get an urgent call back and they have not been able to do much. Maybe contact your MP and get them to help you get an appointment to collect your valid passport from the office you sent it? I am planning to try this if I don’t get the new passport in time. It is ridiculous that there is no system in place for getting your documents back. I feel like it should be illegal.