The only single horizontal motor F3s that is documented is the 2245 Texas Special, and that was only until they morphed it to a single vertical motor under the same number in 1955. This was the cost reduced transition to the vertical motors that you talk about. Additionally, the 2343 was never in a set as an AB. Only AA or ABA.
Since we can't agree on the locomotive, lets move on and see what other things we can use to figure things out. What year was the set gifted? What are some of your cars you think made up the set? These other pieces of information may help things fall into place.