What economic level are the people in your concept? Keep in mind that the average income at that time was very low compared to what we would consider reasonaable. $2.00 a day might be considered a reasonable income. That sort of information you can find. Pullman (sleeping car) travel was for the well off and the expense account traveler. Everybody else would be in coach. Even a coach trip could cost several days wages. I would suspect that it wuold be even more likely in 1933 than later that the coach passengers would be changing cars at Washington DC. It would also be likely that a change of cars at Greensboro would be required. Dining cars also tended to be changed out several times. Most of the coach passengers would be bringin their own food. Dining car meals were expensive.
In addition to the Asheville Special, there was another through train, and possibly another all stops local. The other train was the Carolina Special, which left Asheville about 10:00 to 11:00am, at least in teh 1950's. It connected with the Piedmont Limited at Greensboro, and got you into New York at about 6:30am, if I recall correctly. I know the train got ot Washington DC at about 1:30 to 2:00am, and the southbound counterpart left DC just short of midnight. This train made more stops than the Asheville, but also carried sleepers. I do not think there was a through sleeper Asheville to New York. I think you had to get the sleeper at Greensboro.
Also, remember that train travel would be segregated in that era. Even though teh black population of that part of North Carolina would be fairly low, there would, by law, still be at least be one coach on the train designated as being for "Colored". On branches, and maybe even here, the situation could aslo be accommodated by a "Divided Coach" which would have a partial wall across the coach in the middle, wiht each half appropriately designated.
The coach seats would be of the "walkover" type, not reclining seats. Reclining seats came along later. Even so, these were regarded, at least by my parents, as being more comfortable than theseats in teh Pullman sections when these were made up for daytime use. By the way, only the truly flush or spendthrift would be in compartments or drawing rooms. For the most part sleeping car passengers rode in open sections.
Given the times and conditions, people would take long trips in coach that would be regarded as near insanity today. My mother-in-law talked once about in the immediate pre WW2 time making a round trip from Pensacola to Boston, with three small kids, to be there while her husband's ship was in port. (At that time kids under 5 were free, and 5 to 12 1/2 fare.) We are talking about 48 hours on the train, with changes at Flomaton AL, Atlanta, Washington, and New York. She later made an even longer one: Pensacola to San Diego. We are not talking teh Sunset Limited here, either. I do know that on the trip back it was on teh SD&AE, because she talked about the train looping down into Mexico between San Diego and Yuma. I have not tried to figure out how long that took.