I don't have much experience with soft seated butterfly valves as I don't really ever purchase these. Typically, if I require a butterfly valve for a process service, I default to a triple offset, metal seated, high performance valve and these are typically available to ASME B16.34.
I understand that the most common standard for resilient seated butterfly valves is API 609 and that under API 609, it is not mandatory that the valve meet all the requirements of ASME B16.34. API 609 only references certain parts of ASME B16.34 (e.g., pressure temperature ratings) and not all of the requirements.
API 609 is a listed component standard in Table 326.1 of ASME B31.3 and so these valves may be used in ASME B31.3 piping systems. I assume that the end user has specified the ASME B16.34 compliance as mandatory and so all I can suggest is that you go back to them and tell them that you have been unable to locate a compliant valve and would they prefer (1) that you switch to an alternative valve type (e.g., triple offset metal seated butterfly valve, ball valve, etc.), or (2) that they accept API 609 as an alternative to ASME B16.34.
PS: in the future it would be helpful if you would provide such additional details in your original post. There was no mention of "butterfly valves" until your 4th post.