To update references on change of a global, one needs to do a "redraw" as per the context menu for each component, rather than do this manually, a simple ruby script can be attached to a button as per
https://forums.sketchup.com/t/redraw-all-dynamic-components/77512
https://sketchucation.com/pluginstore?pln=ae_ToolbarEditor
where else a component instance will update to the current global on insert.
Can you share the main focus of your use of DCs? as its quite likely other scripts will be useful.