Service IDIQ with lay in material

I have a service IDIQ for upgrades to a shock strut. The service IDIQ includes the material required to complete the upgrade; however, it's one of those requirements you don't know what needs to be replaced until you tear down the strut.

The last task order was issued during the IDIQ's effective ordering period, but the upgrade service was slow going, and the material required to complete the final task order wasn't requested prior to expiration of the IDIQ's effective ordering period.

What's a fella to do? I know of no exception allowing me to modify the task order to acquire the additional material after the IDIQ's effective ordering period has expired, but to go through the hassle of creating another requirement to procure the remaining material seems a bit much. The material prices were fixed with the IDIQ, and the Contractor will honor those material  prices. Any new requirement would most certainly result in a significant price increase. I argue this is a service IDIQ and we are not acquiring additional services, simply the material required to complete the service they were tasked to perform prior to the IDIQ's effective ordering period expiring. There's no other issue. We're not increasing the ceiling of the IDIQ nor ordering anything in quantities greater than what is authorized with the IDIQ. Extending the effective ordering period is not an option...easily anyway. It'd be easier to make this a separate requirement.

Can we mod the task order to add the material using the whole "sound business judgement, best value to the Government" argument? (I believe there's a caveat to that, in that any such action must not be prohibited, but, c'mon.) Is there some obscure exception that might be worth looking into?