Hi,
In your first mass action, make sure the first action is "update the values" on the column "product_alias" and use the operation mode with the value:
That way, it will auto fill the product alias with the product_code so that it will allow you the saving.
The only have "_copy" in the product code, not in the name. Also, if you move the ones with the "_copy" in the code to the target category, you can then use again the original ones from the first category to duplicate them again in the original category, in order to move them to another target category. So it should not be a problem.