Educate me on why 340 fan is not symmetrical

Blades non symeteric to prevent harmonic vibration at resonate frequency. Do you have the fan clutch for that fan? This fan was used with a fan clutch. The 213 fan did not, used on 1968 340. The issue you will have to address is the distance from fan to radiator which may require a spacer or the correct length fan clutch.
I intend to use a clutch with this application. Noticed the 213 is a 1.5 inch pitch for the 340 and 383 specifically for Barracuda and Dart. Though I want the correct fan for the Barracuda, thanks for your comment regarding fan clutch. Really would like to use one.