On occasion I've had to move t/a monitors to free up a player for reconfiguration/maintenance. Each time I had to re-enter our custom timings for warning/critical thresholds from the default numbers originally set.
Suggest that in the Admin|Settings|WPM Settings|Manage T/A Monitors|Transaction Monitors tab click/selecting one or more monitors, insert a 'migrate' button in between the 'remanage' and 'delete' buttons [all selected monitors be on the same player to enable the button]. Next page to display available players to choose from and migrate/move the monitors to.
There's the matter of keeping historical metrics. Moving [add monitor to playerX, remove monitor from playerY] deletes the history from reports.