I agree that the Gulfside Trail will get you to the Adams neighborhood from Jefferson pretty routinely. Safety-in-numbers-wise, it's plied heavily by AT hikers, Presi and hut traversers.
If on your return from Adams you're not psyched about the 700'+ climb back up Jefferson from Edmands Col, you can consider a 1.5 mile bypass on the Cornice for just a 0.2 mile penalty in distance. It's lightly used and rocky, so as you take it after returning from Adams on Gulfside, you'll notice that it's forcing you into a slower pace -- but in the course of bringing you back to Caps, it adheres pretty faithfully to the 5,000' contour. Just pay attention to the fact that the first junction you get to is with the Castle Trail, not Caps, which comes next (It's a 5+ mile road walk between those trailheads).
Alex