Oh man - how embarrassing. I found out how to fix it myself and will leave this post here for any future searches on the same error for people with a similar setup.
On the Square settings for the individual Gravity Form I had the issue with (NOT Square settings for Gravity Forms), where I had the Square feed set correctly. I had to click on Edit and right down the bottom there was a Conditional option… I had to enable this and set it for the condition that matched display of the Square credit card fields (ie. Online Payment Method).