What is the ruling on wiping the head in this manner, and is it permissible to adopt wiping part of the head to avoid re-performing prayers?

Wiping the head once is sufficient. If there is still moisture on the hand, it should be used to wipe the sides of the head. If the hand dries during the wiping, water should be renewed to wipe the rest of the head. It is permissible to follow those who say that wiping part of the head is sufficient.

Wiping the furthest extent of the hair on the head is sufficient. What extends beyond that to the neck, leaving it unwiped does not invalidate the ablution. It has not been authentically narrated that the Prophet, peace and blessings be upon him, wiped his neck during ablution. Scholars have differed regarding wiping the neck: The Hanafis recommended wiping the neck, the Malikis disliked wiping it, the Hanbalis did not recommend wiping it, and the Shafi'is said that the ghurrah (white blaze) should be extended by washing more than the obligatory part of the face down to the side of the neck.