To summarize: If you had cards in play when the Cleanup happens that end up discarded, you want the game put one of them on top of the discard. If not, and you have cards in hand that will be discarded, let the game choose you which one to put on top.
I have to confess that I'm still not totally sure on what exactly should happen.
While you can discard your hand completely and 'mask' all but the top card, I don't think you can combine this with discarding your in-play cards in such a way as to mask all of your discarded cards from hand. Because we know that in theory the discard of in-play cards happens one at a time, with various things possibly triggering from them (Hermit, Travellers,...).
So I *think* that you cannot hide at least one card discarded from your hand from your opponent. In this case, showing one of those cards on top of opponent's discard pile woule be correct.
Of course, the argument that the discarding player has no control over what that card is is still valid.