Why did you adopt the opinion that water less than two qullahs becomes impure upon contact with impurity—whether it changes or not—despite your awareness of the difficulty of purifying impure tiles?

This issue is a matter of scholarly disagreement. You may follow the opinion of those who hold that water does not become impure unless its characteristics change, which is the view of the Malikis and a narration from Ahmad that Ibn Taymiyyah preferred. Adopting this view is particularly recommended if you suffer from excessive scrupulosity (waswasa). As for impurity on tiles, it is purified by pouring water over it, or by dryness according to some scholars.