You are quite right, both the Earth and the bowling/golf ball are falling toward their common centre of gravity, which for the bowling ball is a tiny bit closer to the bowling ball, so it will hit a tiny bit sooner. However I think the difference is short compared to the length of time it takes light to cross a nucleus.
Probably you are also correct in believing that Galileo would not have thought of this correction (although he might have - one of Galileo's strengths lay in his ability to ignore the details to highlight the fundamentals). However, Newton would have certainly recognized this effect immediately.
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