Hi Tim,
Sorry for the trouble caused at your end.
Per my experience, when you copy the content controls from one document to another document, the content controls will be traveled with the document itself. But, as you mentioned “copied the links into the text “, can you please provide the complete steps taken at your end? It will help us to test in the same environment.
In addition, if possible, can you please share the sample Word document with us to test at our end? You can upload the document to OneDrive and share the link to access it.
Appreciate your understanding.
Best Regards,
Chitrahaas