I'm thinking you're using a freewheel in a 1972 120 OLD frame.
I'm just finishing a 1961 Holdsworth Cyclone - 120 OLD at the back.

I've managed to fit a SunTour New Winner 13-15-17-19-21-28 in 122mm fairly easily with 52/36 at the front.
With the option of 13-15-17-19-24-32 (I've got the gears).

That should cover most 'a few hills' options.

My main bike is 52/42 + 13-15-17-19-21-24-28 7 speed freewheel and works fine but hills are starting to get difficult.