According to EPCRS, Section 13.04, "If the Service and the Plan Sponsor cannot reach an agreement with respect to the correction of the failure(s) or the amount of the sanction, the plan will be disqualified........"

Is there an appeals process that can be initiated at that point?

I don't know of any internal appeal at IRS, but you can file for declaratory relief in federal court under IRC section 7476.