"By default, chown only allows the root user to change ownership of files from one user to another for obvious reasons.
Is there a kernel tweak that can be applied to change this default behaviour to allow users to change ownership of files themselves?"
Not that I know of. Another way to solve the problem could be using group permissions. A user could allow or disallow other users in his group to rwx his files. Also, a user can change the group ownership field to any group that he belongs to. So you could set up a group that only a single user belongs to, say mine and a group that all users belong to, say shared. Then the user who is in both groups could share a file by using chown to change the group name from mine to shared.
Be prepared. Create a LifeBoat CD.