I'd say it depends on what Carter means by
This Zavio does a great job of capturing the license plate, but the reflected headlights complicate Camio's video processing.
If he needs to eliminate or drastically reduce the reflected light because of some technical reason (false motion?), then you might not get there by upping the shutter speed.
In that case you would need more contrast between the visible and IR light, one way to get that would be by external illuminator or possibly increasing the IR power, if configurable.
If the camera is used only for LPR, you could also use an ir-pass filter, though that would be pricey as well.