If you do get the upgrade the documents of yours that are currently in Durham will be sent to Belfast
I think anyone can apply for the upgrade so I don’t see why they wouldn’t accept you getting an upgrade before you apply. As for going to the office I can only speak for Durham helping people who go there in person hopefully other offices are doing the same and you manage to get to speak to someone there.
In my case I went to the Durham office when I had 10 days left until my holiday and had the passport a week before the holiday.