Nothing scientific here but just what I discovered playing around in my "Shade Tree" Welding Art Studio.
Never done anything with this to a code.
In an unnamed plant, on an unnamed planet far away in another galaxy, we were told to weld some S/S brackets to a copper vessel. Modifications were made to the 95/5 Cu vessel so we used the Copper rods supplied and it held up to a hammer test. It really wasn't a test per se. We just beat things into place after the welding warped it out of alignment, and it held.
There is a big issue with "Hot Short Cracking" due to copper and chrome not playing well under excess heat.
Mostly, I was experimenting with this in an artistic application involved joining Silicon Bronze, Brazing rod and 14 ga. copper wiring to 304, 316, 440C and ATS 34. Reinventing Mokume as it were... What I found was that if heat input was kept to a minimum (NOT letting the stainless get too hot) there appeared to be no cracking issues. Using GTAW with minimum amperage and fast travel speed, joining S/S with the Cu based "filler metals" (TIG Brazing as I called it) gave the best results.
Low and high carbon steels such as A36 and 1090 seemed to join well with the copper alloys.
The low carbon, high nickel Austinitic S/S seemed to do better than the chrome-high carbon 440 and ATS34. I can assume this is due to carbide precipitation (sensitization) and that the nickel (which is a magic metal and) in it's pure state is the "Universal" mixing metal to alloy with for most metals in welding.

Of the processes you mentioned, I would save the O/A for a last resort as the high heat input into the S/S is not favorable to success according to my experiments.

Only shade tree advice here as well.

Have made many many argon backing fixtures with copper contact surfaces and stainless bodies.

We used GTAW and both 347 (AMS 5680) and Hastelloy W (AMS 5786) fillers with good results.

I have also in a pinch used GTAW and BAg 8 bare brazing wire

Sorry no code work  :(

Okay, when I looked up my applications, which were from over 18 years ago, it was silver to copper (electrical application).  So different from what you are asking.  We used a copper electrode with GTAW.  Can't find the book I had all my specs written is so am still looking for the electrode classification and welding parameters but may not be of help to you anyway.

Have a Great Day,  Brent