There seems to be a bit of confusion (at least for me) within this argument. While the topic is titled "Shuffle Definition," there's a bit more discussion on discard rules than shuffling, I think.
Taco Lobster's argument (in which I see the most merit) is that there is no rule on how or in what order cards from your hand and in-play must be discarded. For example, if you choose to discard after being Torturer'ed, you may choose the order in which the two cards you discard enter the discard pile, so long as both cards enter the "top" of the pile. That is not random, you chose the order. It is NOT cheating.
I believe the same should be said for clean-up. There is no rule, other than "on top" of the discard pile, for how you clean-up your turn. (Is there?) My actions are lined up in chronological order in my play area, my treasures in a pile below that, and victory cards still in hand. As long as they all go on top of the discard pile (and not the bottom, or cut into the middle), I don't see how an opponent can claim I cheated if I blend the cards being cleaned-up into any order I want. That includes putting the two terminal attacks at the top and bottom of the <i>stack of cards being cleaned up before placing the entire stack on top of the discard pile.</i> (Responding to the original idea of splitting terminals.)
You shouldn't (can't) place one of those terminals at the bottom of your discard pile, since the bottom isn't the top. I don't see why you can't split them up within the same clean-up. To look at it another way, if you were to discard one card at a time, you could do so in any order, starting with a terminal attack as your first dicard and ending with a terminal attack as your last card.