We have concerns about the current state of using the GRA from mobile devices as well. We're currently working on revising the front-end to make it more modern and responsive so that users should be able to easily log minutes and books using the Web browser on their mobile device(s).
A mobile application is on our radar for the GRA but probably not until next year. We could certainly look into building some sort of API to allow minutes to be logged from other applications, I'm just not sure that we'll have time to code it on our end for summer 2016.
Since the project is open source, anyone could contribute an API - once we review contributed code and determine that it is secure and functional, we'd happily integrate it into the main GRA source tree.
It is our intention to post on the forum here as we deploy improved builds of the software for testing. If you'd like to contribute to that effort (just testing the site on mobile devices and providing feedback) it would help us a lot.