It's been somewhere around 20 years since I first / last saw the episode in full, and my memory may not be perfect. But, as I recall, the final solution did not end with the destruction of the Dalek race, and the Doctor knew, or planned it that way (it wasn't just something the BBC cooked up later so they could keep using the Dalek... well, it probably was something the BBC cooked up so they could keep using the Daleks, but they did it at the time, and it was in the story...)

If the Doctor's right (in your quotation above), and touching the two wires together would cause the Dalek's to cease to exist... well, that would be a different end result.

Kiralee