We have 3 cams running at one location that sounds similar to your issue. First cost was a factor. Every vendor tried to sell them very high end cameras that they just couldn't afford for the night shots. They wanted less expensive cameras, yet they wanted good resolution of the plates at night. The best solution we found for the money was to spend a little on lighting and then much less on the cameras themselves. A couple of flood lights at plate level on each side of the gate pointing in a V pattern allowed the cameras to do well and the client was very happy.

I don't know if that's an option for you, but you might consider it.