I think playing a large chain of cards that don't draw to gain information potentially about something like if it is possible for you to empty piles with a chain of remodels is a bit outside the scope of "no information". If you are playing non-drawing actions in a King's Court chain first, that just seems like sub-optimal play to me, but if all you gained were coins actions and buys, and perhaps miscounted something, I would probably allow an undo even if it was several steps. It's a bit of a subjective area.
I certainly hope that no one attempts to abuse a "allow all undo's that don't provide new information" agreement for something like the first example. If the situation occurs, and your opponent feels you are breaking an agreement by denying it, you would need to contact your moderator who can make the judgement call. In the case of any dispute, you can save the game number, and have one player resign with the intent of resuming the match later as described in the rules for handling disconnects. You should also complete the remainder of your 6 games to attempt determining a winner without the disputed game.
If your turn ends, it is a bit harder to undo, but I would still encourage making it happen if your opponent accidentally clicked Duchy instead of Province.
Agreeing to ignore (preferably exclude) cards is fine, and is explicitly mentioned in the rules (7.2).