I didn't look inside the ZEZ much, I just intended to edit Speedwell Street but got carried away a bit. I hope the access tags are correct but as I can't see the signs I just did what I could. There seemed to be a lot of superfluous tags already covered by others so slimmed them down. Are you sure 'psv=yes' is correct given taxis are only allowed for part of the time as per 'taxi:conditional=yes @ 07:00-19:00'?

As for the status, as this is restricted to general traffic and only public transport and occasional delivery vehicles are allowed through, this doesn't seem appropriate for a tertiary route - often designating as you say "roads connecting local centres". This doesn't fit that IMO due to the restrictions.