Is dipping the hands and feet in a basin of water and wiping three hairs from the head permissible for overcoming obsessive thoughts about ablution (wudu')?

The cure for obsessive thoughts (waswas) is to disregard and ignore them, and not to pay any attention to them. Perform ablution (wudu') in a normal manner, washing each limb once, twice, or thrice, and do not exceed that. The strong presumption of having completed the ablution sufficiently is enough. There is no harm in adopting the easiest opinions to repel obsessive thoughts, such as following the view of the Shafi'is regarding wiping over the head. What you are doing by washing the limbs and merely wiping a few strands of hair is an obsessive thought (waswas); therefore, disregard that and perform ablution in a normal manner.