[JKT]

Unfortunately, there is sweet FA that OmniGroup can do here. It is up to EndNote to support OmniOutliner, not the other way around and the chances of that happening are a big fat zero.

You might have better luck trying to persuade the developer of Bookends to add CWYW support for OmniOutliner to their software, but again, it is up to them to add it and not the other way around.

However, you do know that EndNote (and Bookends, I think) are able to use .rtf files (which OmniOutliner exports) with the citations in them as source files to create reference lists? It doesn't update the reference listing as you write, but converts them on the final rtf file.