Pesach is no proof to anything, as the Halacha is to be machmir crazy chumras that are shittos Yachid and would never be kept during the year, if that is your minhag.
http://www.oukosher.org/index.php/articles/single_print/1380207
Ta’am Lefgam is a Machlokes the Rashba & the Ran whether it is no longer Ta’am or it is Batel. Ashkinazim are machmir like the Rashba, and since on Pesach Chametz is not Batel, Aino Ben Yomo may not help.
As usual, AYLOR.
As far as your specific case, you may just want to replace the dishwasher. Compared to the price of a house, the difference between buying new racks & a new cheaper dishwasher is not great.
It should be with Mazel.