I do not believe you will be able to force overexposure of lettered areas using IR diodes alone. License plates are designed with intentionally high reflective contrast in the offset areas.
Even if you could put enough energy into that area, these cameras have switchable IR cutoff filters that are used during the daytime (making this approach only viable at night.)
Another idea: a visible-spectrum laser + camera on a tracking gimbal? Absolutely could block (or even destroy!) these types of imaging efforts on a small scale.