Any time there is a fault, it is detected by the retirement stage as it inspects the ROB. There are already hundreds of state changes that must be rolled back: all of the succeeding entries in the ROB. So the work performed by the recovery mechanism isn't changed by the amount of clobbered state because it is completely clobbered! The ROB must rewind it all.
The register file doesn't need any additional ports, because the fault recovery mechanism doesn't touch the physical registers. It only updates the register alias table (RAT) to point to the appropriate registers. But that machine must be capable of restoring 100% of the register pointers very quickly no matter what. Whether the faulting instruction touched one, two, or 16 registers doesn't matter. The 100+ updates following it are enough state that the answer must be: "Everything".