The more sensible solution would be getting Kinch to re-number the 9 (one single route) rather than an entire network. They also have more numbers available to them that would still see it fit into their Loughborough numbering.
As it's the 9 following the demise of Premiere, when it was Red 9, perhaps it should return to the previous "99" number it had when Nottingham to Coalville was a Midland Fox - Arriva operation.
Alternatively, it may be worth accepting that this doesn't cause on the ground confusion. If you're a visitor to Nottingham, they use differing outbound stops at the main traffic generating end of the route (City Loop or Broadmarsh bus station), different stops at the Railway Station and only after that - where likely local journeys are being made by those who are used to the local network and the two differing colours of buses that each "9" produces, do they start to share the stops.