They didn't end up in any one particular place. In more recent decades, discovered skulls are generally returned to Japan, or disposed of in various ways (lack of identification).
Certainly at least some would have been gotten rid of (through burial or otherwise) since WW2 was still ongoing. American authorities did not officially approve of the practise. Though enforcement of the ban was lacklustre, from the beginning some trophy skulls were ordered disposed of or reburied. In the early post war years, several skulls were discovered both thrown away as garbage or in the possession of former soldiers. Beyond moral implications, possession may provoke murder investigations or breach state laws, all of which encouraged quiet disposals.
Sometimes souvenir skull turn up when the houses of former G.I.s are legally searched for other reasons and other times are found at the local dump, having been disposed of during a move.
- Quigley, Christine. Skulls and Skeletons: Human Bone Collections and Accumulations. McFarland, 2001.
Equally certainly, not all felt such "growing revulsion" at keeping them - at least, not for many years to come. Those trophy skulls which weren't otherwise lost ended in a wide range of circumstances. Some were kept as prized family heirlooms. Others were donated to academia for study or used as teaching aids. At least a few ended up in museums as exhibitions or became apparently traded as collectibles. Several skulls were retooled into decorations; at least one was known to have been fashioned into a Halloween prop with an light bulb.
In one case, a large number of skulls were harvested by a navy doctor. In 1974 he donated them to UC Berkeley for osteological studies, where they eventually became a museum exhibit.
For a long time after the war, these trophy skulls were treated like souvenirs and memorabilia, or simply forgotten in a basement. As the decades passed however, custodians of Japanese remains increasingly sought to repatriate them to Japan. Often this came about as veterans began passing away and their surviving family went through their inheritance. Many veterans, too, began seeing their wartime souvenirs differently than their younger selves.
To some veterans in old age, or to their surviving relatives, their trophy eventually came to seem 'a soldier who rates a ticket home - the 'last prisoner of World War II' as M. expressed it to the Dallas columnist - an actual person wrongfully prevented for fifty years from returning to his own people.
Harrison, Simon. Dark Trophies: Hunting and the Enemy Body in Modern War. Berghahn Books, 2012.
Sometimes, the Japanese government made official requests for the remains, which seems to have generally found receptive ears. However, where the process was initiated privately, the return trip often turned out to be harder than it had been bringing the skulls into America in the first place. Bureaucratic red tape aside, both American and Japanese governments has been reluctant to transfer remains without clear evidence of origin. The US Naval Hospital in Okinawa almost destroyed a skull as medical waste before Okinawa prefecture was persuaded to accept the transfer, for instance.