Think your a bit stuffed really, sticking with the Canal does take you the long way round but at least your safe (from cars).
Got a couple of m8’s who ride to Halesowen on the A456 (got footpaths up to the bypass, if it’s still a bit scary), you could maybe do that then head cross country through Halesowen up towards Hurst Green. Once into Brum you can shadow the Hagley road on the right hand side quite easily (quinton ln/court oak rd/croftdown rd/Gillhurst rd/Augustus Rd/Harborne Rd) & blast through the city centre…
When I lived in Brum I was just off the Hagley Rd, and simply took my chances cycling along it, as usually the traffic pretty snarled up any time past 8am.