One issue is that the GMA_500 driver is actually for US15W (Poulsbo) and not E680 and the GMA tema never did a Linux driver for E680. The main 3d engine is the same, but there are differences in the display engine. Unfortunately, because of the 3d engine IP used in the E680, there is also restrictions on access to the internal owrkings, like the registers.
Two things come to mind:
1. Have you tried the EMGD Linux graphics driver as it might solve your issue? EMGD1.18 just released (is available currently on Intel Premier Support, but soon should be up here at http://www.intel.com/content/www/us/en/intelligent-systems/intel-embedded-media-and-graphics-driver/emgd-for-intel-atom-systems.html
2. Have you looked into the PRM manuals that are published on the 01.org site for other chipsets as the E680 utilizes a newer display engine similar to some of those documented in the PRMs. (https://01.org/linuxgraphics/documentation) or more specifically (https://01.org/linuxgraphics/sites/default/files/documentation/965_g35_vol_3_display_registers_updated.pdf)
Hope this helps.