Just to clarify, when it comes to the email integration, do you have different connectors? Or do you use the “Invite members to integrate personal accounts”, and you need to set the defaults per connected email account?
I ask because I believe these are different things.
I made a similar request here (for import, not sync, but they work in similar ways): When importing data from csv, allow to set a static field value (not present in source data)
For your use case, I am wondering why automations “On Create” can’t solve it? Any time its created, depending on the “Synced By” it sets a value. What do you think? Maybe I misunderstood.