Why would you not consider 307? I agree that 307 is not common on the shelf, but we use ~1,000# of 307 tig rod per year and it's easy to get. We also use ~30,000# of 307 GAMW and don't have to wait for delivery. It's made in Scranton, PA.
I agree with 310 or 312, but if the service temp is elevated I don't think it's a good idea.
The only real differences between 307 and the others is that it has fully austenitic microstructure, more Mn%, and a few % less of Cr and Ni.
We went to 307 a few years ago as a cost save for all 304 and 304L welding, this includes 304 to mild steel. Most of these parts see service temps of 800-1300F without issue. These components don't see a heavy chemical attack thus the mild steel is good for some flanges, the thickness is just increased. 307 has a higher yield strength than that of 308, 309, or 310 (excluding 301H). The high carbon and Cr in 310H brings the yield strength up to within 2000psi of 307. And the even higher Cr in 312 takes its yield above 307.
For a single part or short run, 309 would be easy to get and cost effective, but for higher volume or large wire consumption, 307 is much more cost effective and suitable for the application.