Jim,
Having had a look at the B12 map that Phil posted, I think I got part of the 1945 Ward Boundary wrong. Proceeding clockwise from the Moseley Road/Highgate Road crossroads, it's more likely to be:-
Highgate Road - Stoney Lane - Anderton Park Road - Woodstock Road - Ladypool Road - Newport Road - Kingswood Road - Brighton Road - Moseley Road - Edgbaston Road East - Edgbaston Road as far as the River Rea - Along the Rea to Belgrave Road - Up Belgrave Road to Moseley Road.
It makes that southern 'peninsula' a bit bigger, but doesn't sort out your friend's Taunton Road problem. Neither does it explain Fred's Leamington Road conundrum, unless both scenarios were caused by boundary changes, as wam suggests. I guess Balsall Heath is where you want it to be.
Ahaa, now we are seeing where the memory and perceptions plays tricks on one. Postal Code B12 (before proper new world post codes), was the banker for me. If it was B12 it was BH. As I was posting that street sign for Raglan Street I had thought it carried the '12' sign, like this one of Tanworth Grove (it didn't).
About a month ago, I phoned Adrian Goldberg's Saturday morning radio show, to join in a discusion about how many cinemas there were once upon a time in BH. I didn't, but wanted I to say there was a possible 6 (six). Moseley road had 3, Imperial, Moseley Picture House, and Alhambra. There was the Luxor in BH Rd, the Triangle in Gooch St and finally, The Carlton Taunton Rd. I simply didn't know of the Olympia in Ladypool Road, and didn't enter my head even on Gold's show.
As you've said wam's suggestion that BH is where you want it to be (or not to be) may be the way it actually is. And as wam also intones 'people and organisations rather not be identified with the area'. The Joseph Chamberlain School shifting the border along away to do this.
Trapio, had used the term PNG about people on people, but it strikes the cord for the place as well. Looks like my ex-Taunton Road friend has come out of his childhood years with a preference to be in Sparkbrook.
I was also surprised when I saw the borderline take a left turn into Moseley Rd at the top of Brighton road, I was sure the line would go straight on down Cromer Rd. The River Rea is also a problem for me, even though I accept the river as a natural border.
Finally I have an interest in the placement of a company in Vaughan Street South, K&S Plating Co Ltd (now gone, and associated with the lady that lived in Tanworth), I see it is in Phil's B12. I want it to be in Balsall Heath, because it would suit my purposes.
Jim