Dealing with adtpostalles as a foreigner.

Background: I've been a Swiss resident for a few months, but now am returning to my country (non-European), decided to travel in Portugal and Spain before going back though. As I lived in Switzerland for a bit I had a few bags with me, turned out the cheapest way for me to get my possessions to my country is to send them to the EU and fly them with me when I go back, so I sent them to my final destination in Madrid and have contracted a storage company to recieve them and store them until I get there.

Here's the part I'm worrying about, when my bags were late to arrive I contacted the postal service which informed me they were in the possession of adtpostalles and I need to deal with them.

The company I contracted has been kind enough to give me their tax number so I can open an account with adt and I have provided whatever data I could, although there is no invoice as these are my personal posession and have attached a statement saying as much,

The question: I have one more week remaining in Spain and the documents were provided today, from your experience will I get my bags on time? Do I have other options? I can't send them back to sender as I no longer have residence in Switzerland.

Finally, as this seems like a common sentiment in Spain, screw adtpostalles.

Edit: also for a company what would the Documento de identidad fiscal be?