I have discovered that keyboard shortcuts saved in a .dotm template do work when the template is attached to a document. My problem occurred because I use a macro to attach the template and update existing styles, then detach the template (after which the shortcuts are no longer available). Therefore, it seems that I need to save my keyboard shortcuts in the global template so that they are available when the custom template is no longer attached.

(Leaving a template attached to a document does not seem to cause any technical problems when opening the document on another computer that does not have the template, and I could leave my template attached while working on documents and detach it before returning them, but the documents do not have my template attached when I receive them from clients and should not have it attached when I return them, so using a macro to attach the template, update the styles and then detach it ensures that I don't inadvertently leave it attached when I return documents to clients.)