I don't know. You can amend the constitution without congress, but that would require quite a lot of organization and "grass-roots" (I hate the phrase, but to use another cliche, it's used for lack of a better one) efforts. You could probably get started by picking off a few active and former members of congress to sort of "lead the charge", but the effort would have to be sustained through several election cycles, I think. You'd also have to make sure you leverage the precedent set by the 22nd amendment (presidential term limit).
It's a bootstrapping problem, and a particularly difficult one because there is a reasonable argument against it (people should be free to elect whomever they want).
It'll never happen, that's the reality. I wish it would, but at this point I have very little faith in government, in fact I have none. They're corrupt and the system is setup to keep it that way. The foxes have been running the hen house for a long time.
It's a bootstrapping problem, and a particularly difficult one because there is a reasonable argument against it (people should be free to elect whomever they want).