Hi Corey,
There is object level security profile role which allows for the ability to change the contract owner. This profile is only set to the document owner which means only the document owner has the ability to change the owner to a different user.
I have had a similar situation on one of the projects I have been on and the way we solved is cloning the create a custom object level Security profile and assign "Change document Owner" role. This role needs to be assigned to the user. After which the same user should be able to mass import using the contract document importer functionality to update the master agreements to a new owner.
I am assuming that you have the knowledge of the functionality of contract document importer functionality which is available as a standard solution from Wave 7 on.
I hope this helps.
Regards,
Parankush