Replacing the largest sprocket in the cassette with a larger one? Got this nice old bicycle as a gift from friends, and it has 7 sprockets in the cassette, plus a hub-gear mechanism with three gears (only two of these work though.)





To come to work I must ride about 7 km, last 2km are uphill, and the last 800m are the steepest. Even with the shifts setup at highest torque, I can manage the entire hill, but only pushing myself to my limits. I would like to have it a little easier.

Would it be a good idea to replace the largest cog in the cassette in this old bicycle with a larger one, so that the toughest uphill parts can become proportionally easier?

Some additional photos:
Bicycle photo album
I was surprised to find that not only did they make this configuration, but it is still made and is available as a 3 speed IGH (integrated gear hub) and a 9 speed free-hub. I have seen older Altus derailleurs similar to the original in the photo used with 28 tooth 7 speed cassettes. I would feel confident in stating that such a set up would work here. A quick search shows a wide range of 7 speed units are readily available. Looking at the photo of the front crank I don't think a smaller tooth front sprocket would be available. The prospect of installing a 3 speed front crank would be a interesting engineering exercise.