There are payroll providers out there, that also act as TPA and RK, this may be a more viable option as the mistake is a combination of all parties.
The Plan Administrator should have given the direction to place the salary limit (but they hired a RK/TPA to notify them of this because I am assuming they are not experts in retirement planning and would not necessarily they needed to do this).
The RK/TPA would not be able to accurately perform their duties without due diligence (as mentioned previously) on the match amounts they are given. Assuming they operate primarily on client given data, this can simply be chalked up to "you get what you pay for" many RK/TPAs are chosen for cost alone, yet not all are created equal.
The payroll provider is either incompetent or not knowledgeable. Clearly they would have the capability to implement the Social Security wage limit to prevent tax withholding based on wages, therefore it stands to reason the same standards would be used on the retirement plan to prevent the miscalculation. They simply failed to do so, or did not know they needed to do it.
The resolution unfortunately may fall to the Plan Administrator (the client) to resolve as the RK/TPA as well as payroll provider may have language in their service agreement that exempts them from performing corrections.