Yes, the parallel method is very precise but currently, lightburn supports only parallax for rough positioning. Hopefully, in the future, they will add the option for parallel cameras.
In the video link below you can see the Trotec parallel camera system. The Trotec software works only with registration marks. It doesn't provide the option for large resolution overlays or automatic feature discovery as the more advanced systems.
For wiring the camera directly to the cohesion board - I don't know. I am not familiar with that particular controller. If that is not possible you could use a simple USB hub. That way you could have only one USB cable coming out from the machine.