There was a time, maybe 10 year ago of something like that, when the API standard was based on ISO 9001. They broke away and although there is still some semblance between the two, it isn't as clean of a match anymore.
When it was based on ISO 9001 I consulted for a few API companies, but didn't pursue it afterward.
The most significant thing I can remember is that API required that you explain how you meet every requirement in their standard in your quality manual.
Hopefully there is someone here that can provide more insight.
Start by getting a copy of API Q2 and reading it against your existing documents.