Yeah. It's not EXACTLY secret Santa, cauze you'll know who sent it as soon as you see the return address. But I can definitely keep it a secret until your package arrives. Only I shall know!
And as for me, what about the idea I had before? Once only two people remain for lottery selections, I'll send both of them TWO names, that of myself and of one other person, and then the remaining two can decide amongst themselves who sends a gift to me, and who sends to the other person. Of course, I'll ensure it'll be totally hot babes fighting over me.
Is there anything objectionable in that plan? If there is, I'll sit this whole thing out and just manage it. Let you kids have the fun!