“Just going, brother! Just looking for some place to stop . . . somewhere. We're from Imperial Valley, California. The 'People's Party' crowd grabbed the crops and any food we had in the cellars. Hoarding, they called it. So we just picked up and went. Got to travel by night, on account of the Washington crowd. . . . We're just looking for some place to live. . . . You're welcome to come along, buddy, if you've got no home—or else we can drop you off closer to some town or another.”
The significance in-universe is that they are literally escaping California (and thus heading East).
The significance out of universe is - presumably - as you noted, that it is the reverse of the original. During Oregon Trail days, you traveled West to obtain maximum freedom and opportunity. During the events when Comet got stuck, California became the land of un-freedom and tyranny, with the mid-west being the only free option to escape.