What if I got off in Washington instead? Would it be possible to take the Metro to Alexandria and be waiting for the Amtrak train I just left, to collect my bags and tip the attendant?
No.
Can't get there fast enough by Metro. You have to take a Red line from Union Station to a Blue line to King Street [about 35 minutes, with waiting for the transfer], or take a Rel line to Metro center and hop the Yellow line to King Street [variable, perhaps about 38 minutes, with the transfer wait]. Then you have to allow time to walk from the Metro station under an overpass to the Amtrak station.
[snipped] So if the train arrived at WAS around 7:00, the question becomes could you do an OJ Simpson/Hertz dash from trackside to the Metro and catch a subway in time to King Street. A look at the WMATA (DC Metro) trip planner indicates that one could catch the Metro (Red Line) at 7:12 PM, change to the Yellow Line at Gallery Place and arrive at King Street at 7:44. Then it would be another OJ type sprint out of the station and under the tunnel but in theory it might work.
My prior answer was meant to address only the part in bold above. I tried to snip out the other parts of the Original Post.
If you are looking at train 97, for example, you are talking about a time with high traffic and crowds at the stations. The average time between train 97's arrival in WAS and arrival in ALX is 48 minutes [over the past 10 days, with exception of one day when there was a service disruption]. The shortest time was 44 minutes.
97 reaches WAS near the end of the high Metro commuter traffic, so crowds will be a slow-down at Amtrak Union Station and Metro Station at Union Station in the late afternoon/early evening. Since Original Poster asked the question, I assumed OP was unfamiliar with the wmata trip planner site [where he could have looked up the info] and that OP lacked the SmartTrip card to get through the turnstiles. Under that assumption, OP would have to navigate unfamiliar territory from Amtrak car to station to Metro entrance to get to the ticket machines to buy a paper ticket. At around 7 pm, the machines will have lines of other passengers waiting to purchase, so an added delay there, at least a minute for each person in line ahead of him. Those minutes are significant; I hear stories almost daily about missed connections with Metro trains because the departing Metro train's doors closed while the commuter was stuck behind slow-moving people [often characterized as "tourists"] on the escalator.
The chances are extremely remote that a person unfamiliar with the system could make the first Metro Red after 97 arrives,
then correctly transfer from Red to Yellow, or Red to Blue, and get
both the correct station level and side of tracks for transfer,
and also not face Metro having its own service disruptions [disruptions have happened every day for the past work week] to add the chances for missed transfers. So the probabality of achieving the 32-minute best case Metro-station to Metro-station trip are low . . . very, very low.
Add to that the fact that OP might be able to
run down the escalator from King Street to the underpass, but he'd have to
walk in the underpass at that time of day [the underpass is a narrow walkway, cars alongside, and certain to have other pedestrians blocking quick passage, it is only wide enough for a single pedestrian at spots] and then
run back uphill to the sleeper in order to
be waiting for the Amtrak train I just left
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I didn't address any other part of the original posting because I don't understand what was asked. What I don't get is -- OP suggests being in ALX at same time the train would have arrived anyway. So why should the OP get off at WAS? Why not enjoy an early dinner, go back to roomette to collect personal items while train is stationary in DC, and then be waiting at door in ALX for SCA to open door for deboarding? OP can tip SCA and collect baggage, there's no hassle, no chance of baggage heading south past ALX, cabs are waiting even closer than at Union Station, and Metro Rail and buses are also nearby. And OP has avoided paying Metro paper fare for the dash between WAS and ALX. So where's the point of exiting in DC?