Using Magento2.1.0-rc1 Branch With Sample Data
Using REST API catalogProductRepositoryV1 REF: http://devdocs.magento.com/swagger/index.html Get Key from Admin token API
I've encountered a similar scenario where I want to update prices per website. So to update the price, I've used
/rest//V1/products/
This worked fine.
So I assume you can use this to update product data per store.