Welcome to OpenStreetMap.

I notice you have used the value "designated" for several access tags. Is your understanding of this tag that the highway is only for designated vehicles of that class? If so, the tag value you probably want is private or permit.

A road tagged with e.g. motor_vehicle=designated means that it is designated for use by ALL motor vehicles.

For example, this section of service road leading off the Eastrop Roundabout has had the tags
foot=yes + motor_vehicle=designated + psv=yes 
added to the existing tagging of
vehicle=private + bus=yes + taxi=yes

The sign in the available Bing street side imagery is TSRGD diagram 617, prohibiting all vehicles except taxis and service vehicles. Unless this sign has been changed, the access tags should be only this:
vehicle=private + taxi=yes
(buses and other PSVs are not exceptions and no assertion can be made about foot access)

https://www.openstreetmap.org/way/190893357
https://www.bing.com/maps?toWww=1&redig=0E61462A315B4089ADF0DBB49CFAA9E5&cp=51.527503%7E-0.161855&lvl=19.1&mo=om.1&pi=-1.4&style=x&dir=232.8