Are you using the wrapper navigation page you showed in another thread on this tablet? If so, I wonder if you could enable the Fully Javascript interface on this device and then use a custom script on your page that uses the Fully event hooks to automatically switch which dashboard is loaded in the background.
void fully.bind('onScreensaverStart','todo();') // ver. 1.19+
void fully.bind('onScreensaverStop','todo();') // ver. 1.19+
For example, you could change to a placeholder dashboard with nothing on it when the screensaver became active and then change back to the dashboard you were viewing when the screensaver becomes inactive.
The blank dashboard would still be running in the background, but if it doesn’t have any tiles on it - especially no media tiles - then the Fire tablet would have less to do. 