To speed up the "Transfer Authoritative Primary" process is best after a full backup taken and recognized by the replicas. That way there are less incremental backups to deal with during that process. But there is no way to extend that timer manually.
"Is there a way to compare the "# of Incr Backups" from each replica and the primary to see how far behind replication is if there is a programmatic way to retrieve this information? Is this available via CLI/API?"
There is no way to set the interval differently for each replica.
"Assume my Primary and Replica were behind in replication. If I were to compare the "Last Update" value on the /status page on the Primary vs. the Replica - would that be a way to detect this condition?"
BFER 8958 and BFER 9026 was created as an enhancement request to add cluster information to the GetStatus CLI Sysadmin command and has been added to the 918 release.
To monitor the replication of a TPAM appliance view the Cluster Management menu then click on the Logs tab. The logs tab displays data pertinent to the high availability implementation on the appliance. Items such as replication status change, failover, etc are displayed in the logs. The Logs tab always displays logs from the primary appliance, regardless of the appliance selected in the cluster member list.