There is quite a lot of variation in tyre size/shape for a given size between manufacturers, and more than 2% change in circumference between 7mm tread and legal minimum.
The Bridgestone RE040 have quite a square shoulder compared to the Pirelli & Yokohama I've also had, with a resultant stiffer ride. The alloy protection is down to design, Avon ZV5 has rim flange protection which actually sits well on the rim, protects from scuffs and does look better as well as the side wall is flat and does not curve in to the bead.
These have all been on a GD1 with 15" alloy where the choice is also limited and the wider tyre is cheaper.
Would stick with recommended sizes on all versions of the Jazz, with pressures at top end of range.
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TG