I did some more investigation, and it appears as though the elastic modulus G varies depending on product form. Both Allegheny and AK Steel (see link below) give higher values for G, 82 GPa and 77 GPa respectively, but they produce flat products like sheet, plate, & strip not long products like bar and wire:
Now, all spring references that I checked (SMI Handbook, SAE HS 795, Rockwell Mechanical Spring Design Guide, etc.) use the value of 69 GPa or 11 x 106 psi for the value of G for austenitic stainless steels like Type 316. This is confirmed by some European spring wire producers of Type 316 (EN 1.4401) like Ugine and Sandvik:
Also note that the strength and moduli increase after tempering, so the value of 71 GPa is probably the most appropriate design value for a spring using Type 316 wire.