The NACE MR0175/ISO 15156 requirements apply to all equipment including pressure vessels. However, if you look at the tables for Austenitic Stainless Steel Materials in Part 3 of this document (e.g., Table A.2), the particular note is that the materials shall be free of cold work intended to enhance their mechanical properties. Consequently, some latitude is permitted.
I have not specifically dealt with this issue before but I believe it is common to form the heads and shells, solution anneal after forming, and then resize to correct for distortion that might occur during solution annealing. There is little you can do about the resizing but I think this is what is normally done under the premise that it is not a significant amount of cold work and it is not intended to enhance mechanical properties ? You might want to review the NACE/ISO interpretations and see if this is specifically addressed.
You might also want to review the service environment limitations of NACE MR0175/ISO 15156 Latest edition (In particular Table A-2) to see if the use of Austenitic SS is permitted in your application. The current document does have some fairly severe limitations on the use of Austenitic SS in sour service.
Keep in mind that free advise is worth exactly what you pay for it and I have not specifically dealt with this before.