Yea, I have the same problem...I didn't claim all of my GS Rewards, so on my Main Server That I play on (Star Forge) one of my Alt Characters got like 7-8 emails with the Unclaimed Rewards, but I'm still missing many more (like the actual Companion, Some the Retired Cartel Crates, the other Armor set, etc)
So I guess I will have to check the Characters I have on the Satele Server (which I never even attempted any GS missions on, IIRC) before msg EA/BioWare...thanks