Sync Record Smart Service - Service Backed Record

We have configured a service backed record with full sync configured. We also have a use case of syncing the changed records after the put call of that service is successful. In the put call process model, we have used Sync Record smart service and have passed the identifier into the node. Our sync expression uses token as an authentication to the service. This configuration works smoothly in dev environment.

After deploying the code to QA environment using a Deployment Admin account , our sync record smart service is failing. The error is of failed authentication. (To cross verify, we passed the same identifier to sync expression manually and it returns the row) The Deployment Admin does not have a valid token to successfully call the integration. To resolve that we have configured the smart service node to run as whoever started the process. Even then the sync is giving error of authentication. We checked in System logs and even there we didnt find any additional information apart from authentication error.

To temporarily resolve it I have published the Process model in QA from my id, but we cannot do this in PROD. Is there any workaround to run the sync node as whoever started the process, basically the loggedInUser?

Note: Deployment Admin is a system admin and has viewer access to the record so there is no security access issue with the record type. And we cannot provide token for the deployment admin.