Replacing the largest sprocket in the cassette with a larger one?
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.