It seems like a non-profit could handle this role where they act as a proxy where the victim of the notice asserts they have copyright, sends the information to the proxy and then the proxy acts on their behalf?
The "act on their behalf" might be considered legal representation. As I understand (IANAL), the EFF as an organization doesn't provide legal representation to others, and more commonly refer them to a lawyer or law school clinic for further assistance.
Righthaven got struck down because they were only assigned "right to sue" and not ownership or exclusive rights to the copyrighted work.
If he were to fully assign the copyrights to the EFF, they would not run into the same trouble Righthaven did.