As I suggested
earlier, put the score on the driver station, and have it published by the field management system.
I hadn't thought about the effect on the human player of adding another display for the score by the clock, but I'm sure this could be mitigated by creative positioning. It would definately make the clock/score displays stand out from team numbers better when there are two displays there.
Either way, the use of the big screen to get the score is really not ideal anyway, because no venue is the same. Putting it with the clock as part of the field and/or on the DS would give each venue more flexibility with their big-screen placement.