In my opinion, API-579 is not presented as a short term stopgap to last you until the next outtage.
The Foreword of API-579 contains the following sentence:
"This publication is intended to supplement and augment the requirements in API 510, API 570 and API 653: (i) to ensure safety of plant personnel and the public while older equipment continues to operate; (ii) to provide technically sound fitness-for-service assessment procedures to ensure that different service providers furnish consistent life predictions; and (iii)to help optimize maintenance and operation of existing facilities, maintain availability of older plants, and enhance the long-term economic viability."
The term "life predictions" says to me that 579 is intended to be used as a method to predict what the remaining life of a piece of equipment might be, whether that is 2 months to the next outtage or 30 years.
The phrase "enhance the long-term economic viability" also seems to state that the methods in this document can be used to support the usage of equipment over a long period of time.
I completely agree that the first step is to check with your jurisdiction to see what methods or documents they allow for rerating.