You would most prob have to use an Update ticket api. 

https://api.freshservice.com/#update_ticket_priority

I cannot see any function for this so not sure if this will work but maybe try approval_status could work as it is in other sections as an option. (Create Service Request)

https://api.freshservice.com/#create_service_request

{ "approval_status": 2,

}

I've never had an issue with approvals lingering when a service request is canceled or deleted.

If the request is canceled our approvers don't get alerted consistently to approve things. Is that what you are experiencing?