The pilot of the Bellanca 7GCBC reported flying the airplane about 8,500 feet msl on an eastbound heading. He entered a canyon, and not believing he had sufficient clearance to cross over the ridge, began a 360-degree turn to gain altitude. During the turn the pilot reported feeling the airplane sink; he then attempted to guide the airplane westbound down the canyon and away from terrain. The airplane continued to descend and impacted terrain at the 8,300-foot level.