We did this last summer (2015) but at the time we were living in MD so it was fairly easy to get to the VA station. We had a ton of Amtrak points from work trips, so we mostly paid with those. I would not have paid cash - it was a neat experience but was not worth what it would have cost using real money. Part of the reason we did it was that the trip was a split stay between VWL and Vero Beach so we would have had to rent a car had we not brought our own.
Boarding was uneventful. On both ends the station playgrounds were closed. We had a family room with a bathroom and bunk beds. We slept very well, we're not bothered by train noise. I would not do it without beds, unless you are a fantastic sleeper in public spaces while sitting up, or don't mind being tired when you arrive in FL.
Our train arrived on time in FL. We paid extra to be one of the first 20 or so cars unloaded so we did not wait on either end. Our rain was very full, so I imagine if your car was later to be unloaded it would have been a good 30-40 minute wait once the cars started being unloaded.
Food was fine - pretty typical Amtrak food - not quite as good as Acela business class meals. Eating in the dining car was a fun experience. Dining times are assigned when you arrive at the station, so if you have kids and want to eat before 10pm you'll probably want to get the the station earlier then you would otherwise.
Our then 3 year old enjoyed taking the train and sleeping on the train. Happy to answer any specific questions you have.