But, unless they have extended the bikes-on-trains policy to include large motorcycles, that doesn't do much to assist a would-be tag mover.
Saturday and Sunday mornings, early (before 9-ish), will be the best times to move the tag, or after 9 on weekend evenings. I wouldn't get near the place during the week, except perhaps in the very wee morning hours.
Despite its tiny size (about ten miles square originally, before the part originally carved out from Virginia was returned to the Old Dominion) there are lots of potential tag locations. For all its political issues, of which there are many, the District has a dense concentration of places of interest (a number of which were good for bonus points in the 2015 Iron Butt Rally) as well as many fascinating neighborhoods. Whether that's enough to draw tag movers is something I guess we'll see in the coming days, weeks, and months.