When you say an IO-360, do you mean the 180BHP version or the 200BHP version ? As I believe the larger one as fitted to Bulldogs are actually a bit bigger. The G-RVVI that Jerry Parr built has one of those and has a non standard bulged cowling ? Not sure if the PA28 Arrow with both the 180 and 200 are in fact the same engines. One of the main differences are all the ancillarys.
Have a look at the Lycoming website for all the differences.