Heating and cooling rate is not an essential variable under ASME Section IX. And while a requal is unreasonable (not to mention illogical since the argument could be that their assumption is that slowing down the cooling rate will somehow improve performance or properties-through some desirable transformation product or lower through thickness stress I assume, but if your properties are already PQR demonstrated as good enough what's the point?-and if they're concerned about long term properties like creep how will you verify that with a requal?) if it is their requirement to requal when it is not a code requirement then they should pay for it.
If they're paying, I'd do it. Of course, sometimes if you use the delivery schedule impact argument the requirement goes away.
In other words, you might find relief if you can get the decision to the money guys instead of the welding engineering eggheads.

The cooling rate is not a critical issue if the PWHT is less than the lower transformation temperature if the microstructure is the only concern. Heating steels to less than the lower transformation temperature  results in reducing hardness and tensile strength.

Hardening is an issue when the base metal is heated sufficiently to form austenite. The alloy content and the cooling rate (from austenite) will determine the microstructure present in the base metal at room temperature, i.e., will it consist of martensite, bainite, pearlite, or ferrite and how much of each is present. The steel can be tempered by reheating it from room temperature up to temperatures between 400 and 800 degrees F. Tempering will remove hardness, it will not increase hardness. Likewise, stress relieving is performed at temperatures between 1100 to 1200 degrees F (give or take a few degrees).  Still, the heating simply removes more hardness and reduces the tensile strength further than tempering. It also allows the residual stresses to redistribute. The residual stress is approximately equal to the yield strength of the material at the stress relief temperature, i.e., higher S.R. temperatures reduce the residual stress faster than lower temperatures. There is a time factor involved, but the most benefit of S.R. is derived in the first couple of hours.

However, rapid cooling can cause unacceptable distortions due to the uneven cooling of thin members and thick members. Slow cooling will minimize distortion by allowing all thicknesses to cool at the same rate. This holds true for the temperature ranges used for tempering, stress relief, and PWHT at higher temperatures. There was a thread a while back where it was shown that a delta T (change in temperature) from one region to an adjacent area of about 220 degrees F is sufficient to induce residual stresses on par with the yield strength of the steel base metal, i.e., distortions will result. So, the cooling rates should be slow enough to ensure even cooling in both thick and thin members. 

While the cooling rate may not be an essential variable from a code standpoint, the engineer, designer, and fabricator have to look at more than just the microstructure of the final weldment, they have to consider the final dimensions of the weldment as well. The code dictates the minimum requirements that have to be met. If those requirements are met, you have complied. If the clients wants more than what is required by the code, it should be stated in the project specifications. Otherwise, I would believe you have a good case to request compensation for the added testing.

Best regards - Al