It appears, based on your comments, that you confusion lies with what actual function a LPS has verses the function of properly bonding the LPS to other systems and other metallic parts of a structure.
I'll also use an example like yours above to see if I can help you understand, but instead of NJ/PA, I will consider my own back yard here in Florida where the strike density of lightning is perhaps three times greater than where you reside and work.
Let's say we have two of these copper cross structures in a large open field, no trees, no other tall objects for hundreds of yards. We place the two structures 100' from one another. On one, we attach a strike termination device (lightning rod), a down conductor, and a connection to a ground terminal (ground rod). On the other one, we do nothing.
Now bring in a storm. The physics that support the early formation of lightning is very theoretical and even controversial, but what can be said is that at some point in the cloud structure, a build up of charges begins a stepped leader approach towards earth. At this point in the sequence of events, earth nor earth bound objects have an influence or direction on where this leader forms and extends. At some point, the attractive forces brought on by the approaching leader begin to strip charges from earth bound objects, including our two copper structures. These charges form streamers, which extend upwards towards the sky. Eventually, a streamer or streamers connect with the downward leader, and the flash or several flashes occur.
Now, back to my opening paragraph. What possible effect does the LPS on the one structure have over the lightning event verses the other with no LPS installed? Nothing. It is possible the air terminal on the one structure may effect the formation and characteristics of its streamer, but it certainly doesn't prevent it from forming.
The fact is that even in Florida, and even during a storm, and even in an open field, the probability of one or the other structure from being struck are effectively the same. Possibly as high as one in a million. The LPS on one does not change the strike probability. It does nothing to stop a leader from forming in a cloud, it does nothing to stop the formation of an upward streamer, and it does nothing to stop the flow of current when the connection between the two is made.
The one and only function of the LPS is to POSSIBLY direct some or most of the surge event away from the structure through an intentional path to earth. The only time the term "potential" comes into play is with the bonding of other systems and metallic parts.
Bonding helps prevent the possible side flash or flash over of surge current from on system to the other or from one object to another. By bonding all the conductive objects together, inductive effects are reduced and no potential is created. While this is one of the most important aspects of the LPS or any other electrical system, it has nothing to do with whether or not lightning will strike.
It is important that you understand what an LPS can and can't do, and you especially need to make this clear to your customers you sell these systems to. If they are under the premise that the LPS system you install will prevent lightning from striking their structure, you have failed them. If they are under the premise that the LPS system you install will absolutely prevent the structure or their equipment from being damaged during a lightning event, you have failed them.
The components of a good LPS start with good luck. As crude as that sounds, it is true.
Please feel free to PM me if you would like some suggestions on good books and websites for the study of lightning and lightning protection, or if you would like to discuss the life and times of Franklin and Edison.
Take Care.
