The clause at 52.243-1 Alt III cannot be used to extend the period of performance because that is not listed as one of the "in-scope" items. The clause at 52.211-13 is not applicable to A-E contracts. If the contractor is not at fault, a bilateral modification (supplemental agreement) per FAR 43.103(a) using the SF 30 can be used to extend the period of performance. You would insert "mutual agreement of the parties" in block 13C.