Seeing through library when only instructed to shuffle?
I agree with Matthew on this not being HCE
HCE is supposed to be applied in cases where we can't correct the error with only publicly available information. But in this case, even if we have perfect information, there's no way to “undo” the error of the playing gaining access to information they weren't entitled to have (in this case, what cards were exiled with Bomat courier)
Also, I don't see how any of the remedies of HCE could apply in this situation, since we have no extra cards in any set, nor any failure to reveal. I guess what you intended to do is to reveal the whole library to the opponent, maybe only the cards exiled face down or maybe even both, shuffle them and go on with the game. To me, this looks more to what we discussed some days ago in another thread, when someone suggested that if a player commits LEC while shuffling their opponent decks before the start of the game, we should just reveal a card at random from their library as a way to balance the advantage gained to both players. And as it was said in that thread, that's not the idea behind the remedies we apply. There are some cases like HCE where we want to neutralize the potential advantage of the player committing the infraction; but even in those cases we don't have the opponent draw an extra card to offset the advantage
I'd just go with LEC, and even GRV looks like a better fit as a “catch-all” infraction
PS: Maybe the intended remedy was to reveal everything and now the opponent chooses which cards were exiled with Bomat courier? I think that would be too disruptive and not really correcting the game state. Plus, the sets were never joined, so I just don't see it as an option