Two shows about the same character (essentially)? I like a good spin-off as much as anyone else, but Torchwood and SJA at least followed new characters that weren't the Doctor. How would a spin-off about the Doctor be different than Doctor Who itself?
The character has the same name, but I've always thought that they were different. Tennant's Doctor is nothing like Eccleston's Doctor, for example. If people are confused by the show that, as you say features the same (but different) characters in different eras of his life, than they don't know much Doctor Who.
So the show would have to be made for dedicated fans? And how long do you think a dedicated super-fan show like the one you describe would last?
I like McGann's Doctor, too, and was there when he debuted on TV, and wanted it to take off. I'm glad his Doctor got a second airing, so that his life is bookended. But I'm not sure that any producers have the interest in running essentially the same show twice. Spin-offs are about broadening the universe, not running the same show in parallel.