I'm facing a similar obstacle with a new ecommerce project.
The project is a front end to a full-fledged store management software (CMS+ERP+CRM). It needs to use the master product database, but have its own entries for product reviews, ratings and so on.
The initial thought was to make a cached copy of the master database. The website will benefit from fast loading times for the cached items, but the implementation is not trivial.
After some considerations, the selected approach was updating the website's DB from the management program. This way the website's copy will always be correct, and most of the implementation doesn't need to worry about REST services (it'll still be used for user registration, shipment tracking etc.)
In your case, where you can't have the service update your own database remotely, you need to come up with a mechanism that allows you to refer to REST recourses like regular models, and that caches them in the background.
Important note: research for a way to make sure the cache is always correct (non-dirty)...