FWIW I do not think there is a particularly good way to work around this. The available options include...
If you use Insert->Quick Parts->Document Property and then choose something like Title or Subject, the the Content Control will be a plain text one. In that case, bookmarking either parts of the text or the entire text within the control is not allowed (i.e. bookmarks are really a "rich text" feature. So any bookmark has to be applied to the whole control, and that means that any { REF } field will "pull in" the control as well as the text. It might be handy if there were a field switch/option that would let you avoid that, but there isn't.
In some circumstances you might be able to use a STYLEREF field to get the text and not the content control - your content control would need to be on its own in a paragraph with a style you don't use elsewhere, let's say "mystyle". Then you could use { STYLEREF "mystyle" } to bring in the first 255/256 characters of the text. But then people editing the document wouldn't be able to modify the reference anyway and you might as well just use another copy of the content control.
To use a REF field to reference all or part of the text without pulling in a copy of the control, you would have to insert a rich text control, then bookmark either parts of the text or the whole text. Even then, if you make a cross-reference to a Heading style, Word will probably create a bookmark that includes the content control - instead, you would need to make your own bookmark to avoid selecting (say) the final paragraph mark. Or bookmarks for the parts of the text that people want to cross-reference. And that in itself is a maintenance problem, because someone modifying the heading text has to know what bookmarks need to be restored if they are deleted.