It IS Late Surrender
The game that is detailed by the original poster is, in fact, late surrender, not early surrender. That was pointed out to him elsewhere in the thread. Notice that he describes "early surrender" as being able to surrender before you take a third card. Of course, real "early surrender" is the ability to surrender before the dealer checks for naturals, and does carry a higher player advantage (or lower house advantage).
By the way, I didn't just deduce this from reading the post and the subsequent responses. I know the rules of the game in question from personal experience.