You can cross North Capitol via the Rhode Island Ave and NY Ave overpasses. The runners will be below you on North Cap.
I'd do that and then grab the 395 entrance at NY Ave, go under Congress, and keep on 395 over the bridge into VA, then transfer to the GW Parkway.
See here:
https://rnr30-compgroup.netdna-ssl.com/wp-content/sites/13/2015/04/DC_18_CourseMap.pdf