I have to say, I've never got the "teyn" spelling. Despite having lived my whole life in Northampton, having a bit of a local accent myself and having parents that come from generations of Northamptonians (whose accents my wife regularly remarks on the broadness of) I've never picked up on an "ey" sound in the middle of the word town. A slightly cropped "ow" maybe or even an "ew" at a push, but not an "ey".
Same here. I'm a Northamptonian and don't get it either. A bit like that song "to his horse" or whatever it is. I never get that either and I've been supporting the club for over 40 years. Maybe someone could explain its relevance to NTFC?