You followed the instructions in the support article right? I did this yesterday, making a brand new account specifically for GOG version, and had no trouble.
Just make sure the Spore name you choose ingame matches whatever name you gave your account on the EA site. If you don't it likely won't realise they are the same account and will give you an error.
Support article reads:
1. Go to https://myaccount.ea.com/cp-ui/redemption/index
, log with your EA data, redeem all three codes (you can find them under more -> serial keys). IMPORTANT! For base game, make sure to redeem actual game and not the Spore Community Access.
2. Run the game.
3. Choose "Register" and log in with your EA data.
Thanks! I couldn't find the info you described under Support but followed the instructions and it seems to be working now. :)