At work we have a system that has a decent API and even has a Laravel package maintained by a community member. I've used it to make a few public facing tools like a check-in system and barcode printing system, and the only Laravel schema is for user accounts.
Overall it is super quick and works fine, but I'm also missing out on all of the awesomeness of Eloquent.
Most of the data I'm reading from the database only needs to be refreshed once or twice a day, so I'm considering writing a sync tool to pull all the data I need and insert it into a relational database, but then when someone needs to write to the database I'd hit the API to submit the data, then re-pull the related data into my project.
This would reduce the number of external API hits my system needs to make, and might lighten the load of the main application, but it also adds a little bit of complexity.
Have any of you written an application primarily for interacting with a 3rd party API? If so, do you sync data and interact locally, or do you make each page load hit the external API?