Unfortunately there is no option to change date format in form data. As you have noticed this is always saved as US format no matter what locale is set in the SharePoint site.
The Date format is saved as invariant so that when Nintex Forms displays it back, we always convert it to the current culture format in run time. This is how the product is designed.
In my opinion, we need to consider a better way to make the two different products more compatible. Please raise this in our user voice site (nintex.uservoice.com) and in the meantime, I will also raise it with the development team - the more weight for the request, the better.