What you are describing is the "Low Elbow" style of Lefty Kreh. The style you learned is the elbow forward style.
Since Steve Rajeff, one of if not the best caster in the world, uses the elbow forward style, you might do better to improve the style you are using than to learn a new style. I think it is not the style of casting but the mastery of the style that determines the distance you can cast.
"This is the arm style of people who have most influenced casting in California, including Jimmy Green, Mel Krieger and Steve and Tim Rajeff."
Both the Elbow Forward style of Steve Rajeff and the Low Elbow style of Lefty Kreh are described by Al Kyte in Fall 2002 issue of The Loop
Lefty Kreh claims his style is easier on the body, however, studies have shown this is not the case. There are fewer injuries of the elbow and wrist with the overhead style compared to the sidearm low elbow style.
"A team of researchers is studying the biomechanics of fly-casting at Montana State University, Bozeman (MSU)….. Elbow pain was significantly less for the overhead style compared with the elliptical style. Wrist pain was significantly less for those who used the overhead style instead of either the elliptical or sidearm styles."
If you want to learn from Lefty, he has a Casting DVD
and a book