I agree re: Squarespace should be fixing this problem as part of their service offering.... incredibly frustrating.
I've been playing around with Data Highlighter but for the most part every page is recognised differently and I can't get the information into product page that Google requires.
Have been trying a few different codes but even though every product page is set up the same in my Skye family, Indigo template it doesn't recognise these on any duplicate page.
Sadly about to give up... disappointing that Squarespace can't provide the fix for this.