First up, I finally found an actual New Haven Railroad Switchlist. It's too big for my scanner, so it's at Chris' waiting to be scanned. I already knew what they looked like (and the form number) because there was a picture of the "old" one in a booklet about the installation of an IBM computer system c1947 (available here thanks to John C. Carlton).
But what I found after that was a form that I didn't know existed:
Note the "Order No." field, with instructions at the bottom. These are generated sequentially through the week, as needed. It identifies where the car is located, where it will go, and the conductor needs to complete the placement time when complete.
Based on what I'm learning from Dale over at the CNZR and Joseph at the Pioneer Valley Railroad, there will be priority switching orders (such as perishables, the freight house, and industries like Stanley Works), and regular switching orders. I don't see anything on the form to indicate this, so it will probably be something more informal.
In the meantime, time to get working on the infrastructure so I can get back to operating.