Forget the PDF/X-1a setting. Use the High Quality Print setting.
Then, in Acrobat, use the Convert Colors feature to convert the document's colors to U.S. Web Coated SWOP (v2). Make sure you do not check the Embed option for the profile. Check both the Preserve Black and Promote Gray to CMYK Black options. Then press OK and acknowledge that the changes are permanent.
Save the resultant file. It will be exactly what your publisher is asking for.
- Dov
