I think I should be fine w/ fitting the 6950 in my case, at least based off this one newegg review of the Atec 300 Mini Tower.
"Pros: Fits a Hyper 212. Great cable management. Fans run silent at medium or lower power. Airflow. Fits my 10.5 inch videocard with room to spare. Didn't need to cram, jimmy or shove anything into place.
Other Thoughts: GIGABYTE GA-990FXA-UD3 AM3+ AMD 990FX HIS IceQ X Turbo H695QNT2G2M Radeon HD 6950 2GB KINGWIN ABT-850MM 850W AMD Phenom II X4 975 Black Edition Deneb 3.6GHz G.SKILL Sniper Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1866"