I also remember Dave Vollmer reporting that his Juniata Division had a sag. I don't remember having this problem on the Virginia Central, although I never put a straightedge on it. However, I glued and screwed the 1/4" Masonite fascia board to the door edge of the VC, and that must have provided some lateral strength. I will do the same to the A&R, once I figure out the scenic profile on all sides. Perhaps, Brian (RockGp40) could shed some light on the VC's current state.
That said, I'm with Lee. I think the 1"x3"s on edge on Chuck's layout will provide more than enough strength. However, for just a few dollars, by taking Chris' suggestion, you will have some joists that could be drilled to provide some support/security for your wiring. That was one thing I could have done differently on the VC. My wiring hung down under the table, concerning me during moves. I haven't fully resolved how I will run the wiring the A&R. I'm actually tempted to take a hole saw to the bottom of the door every 12" or so and attempt to run wires through the core of the door, by taking a fish tape or coat hanger to fish the wires through the cardboard honeycomb inside (or whatever the heck is inside this HCD). Stay tuned.
My suggestion to Chuck would have been to cantilever the door on all edges from the 1"x3"s, allowing a setback, so that your table legs aren't so close to the edge, where they could get kicked.
DFF