First of all, no, the perigee need not be "below the original orbit", where did you get that? The correct thing to say is that the new orbit's perigee cannot be any lower than the location of the collision.

But more generally, how does this justify your claim that "Fragments that are ejected from the collision cannot have more than energy than they had originally"? Or were you conceding that point and making a different point?

See also my more-detailed cousin of this comment.