Call recorder guy and IT guy spent some quality time together on this. They did not come up a solution.
The caller ID info is not present in the sip invite message header, which is where their software needs to see it.

After a couple of calls to NEC support, I talked to someone that said NEC proprietary sip is not going to be in the invite. We need to have a recorder that can understand NEC sip, or the recorder currently in place needs to be correctly setup to handle this.

The recorder is an Eventide Nexlog DX. The company tech that installed the recorder says they have had Eventide looking at this, with no results. They are already using the NEC template.

NEC and Eventide are both very big companies. I don’t know why it is so difficult to make their equipment work with each other. This can’t be the first time this scenario has happened.