I believe production 340s were equipped with a single Carter AFB or AVS. The Thermo-Quad was an aftermarket carb which may be what you have on your motor.
Edelbrock markets repro Carter carbs, manufactured by Weber USA.
So, what are we talking here? My fantasy/nightmare would be a 340 Duster painted in 'Plum Crazy' with flat black hood panels and R/T stripes. Big-azz bright-yellow Lakewood ladder bars to tame the axle tramp and windup that is the natural product of horsepower, a solid rear axle, and leaf springs.
Sooo... Whatcha got?