I have welded with ER320 and learned the hard way that it will crack like glass if the heat input is too high. It is not like the typical 300 series weld fillers. Forget the austenite-ferrite arguments. Composition is nominally:
Cr - 20%
Cu - 3.5%
Fe - 36.5%
Mo - 2.5%
Nb - 3.5%
Ni - 34%
The 300 series stainlesses are typically 18Cr-8Ni with Mo, Ti or Cb additions. ER320 is used for welding Alloy 20 (Carpenter 20). We use it in sulphuric acid piping for water treatment plants. I don't see what your customer is gaining by using it for 316L base metal (other than higher cost and pain in the rear to weld). You will have to limit heat input to 35,000 joules maximum to keep it from cracking and no preheat should be used. Remember, heat input (in joules) = (volts x amps x 60) divided by travel speed (in inches per minute).
Here's a link for welding technique for Alloy 20 that should help:
http://www.alleghenyludlum.com/ludlum/Documents/al20%20(053106).pdf