Might be better suited in the CS forum, but still, if you enchant an item actually a new base item is created. So this will not be of any help for this issue.
I don't know how to solve this issue, as my CloneForm approach in my race control scripts is underlying the same restrictions, breaking scripts checking for a certain BaseID to be equipped/worn.
If there was a simple way, preferably even getting away without having to change the checking scripts themselves, I'd literally die for knowing it.