They were very clear with Dor Yeshorim: The whole purpose of giving your SSN is in case you lose the ID number. Seems pretty logical to me that the SSN can be used in its stead.
If you want to be retested, then just look at your local yeshivas. Most Beis Midrashim do Dor Yesharim every other year. Ask around. (Yeshivas are cheaper, about $150 if I remember correctly)