Try opening a new Word document using your template. Then from the main menu:
Insert > File
and select the files you want to apply your template to. You can select more than one with the Ctrl key.

If you select many files into one you can then cut and paste them into separate files once the formatting is the way you want it.

Your template's styles and the inserted file's styles will both display.
You can now select the styles from original doc. and change them to styles from your template.
After all is formatted you may still have to delete some styles using organizer but it would only be once or twice depending on how many files you combined into one.