Well, the super Orthodox Jews have a solution. Yes, you should make a good faith effort to eliminate all of the hamets in your house, but you can exploit a loophole! Hamets in your house, but not owned by you, are OK, so rabbis in these groups have a list of non-Jews willing to buy all remaining hamets in your house for $1.00 (or other small amount). They then own them and you are in the clear. There is a special term for these people, but I don't remember it.
But what if you later (after Passover) find a box of crackers you missed and you actually want them? No problem because the loophole has a loophole. The buyers don't actually pay you the $1.00, they just pay you a penny as a down payment. As part of their service, they then deliberately don't pay you any more, default on the contract, and, the day Passover, the box of crackers are actually yours again.