I still am surprised that I got my bag when I did. I was getting nowhere with United or AirEuropa (two different alliances....like your situation). 4 days later, I was sitting in a great restaurant on the coast when my phone rings and it is a Madrid number. I answer it and a lady says she works in the Madrid Airport and has my bag. I assume she got my phone number off the bag tag or my tag.
She asks if I have filed a lost bag claim. I tell her the lost bag claim number and she says "great! I will get it over to Air Europa". Suddenly, all the gears start coming in motion and (it still took a day) I eventually get my bag flown to AGP and delivered to Mijas.
But she had NO IDEA that there had been a claim filed. The airlines don't share this info with each other.
But what a hassle. No communication between the airlines, but the bag eventually made it to the destination on the bag check tag.
Good luck!