A wider tire might make less of a tire mark on grass, but I don't think a inch or two is gong to show much improvement for the money I may be wrong. Wider and tall would certainly aid on ride comfort as well.
There is a real struggle when your talking compaction and traction. To get the best of both worlds is a constant struggle. To much weight on the front tires will then lights the load on the drive wheels hence you loose traction on hills and slops. To skinny of tries on front or back will cause the same proportional to over correction. It dont take much to change a Z's handling. Just try out the many types on hills and see why some love or hate the hills and slops of one over another. It is very tricky to get the best of both worlds. "Traction or compaction weight distribution".