[edit] Okay, you've defined it, although pretty much all semi-auto rifles have magazines; I think the distinction you're after is whether they have detachable magazines, which affects how fast they can be reloaded. What you're asking for goes far beyond the 1994 assault weapons ban.
Furthermore, by "ban" do you mean grandfathering in old firearms, like the 1994 ban did, or would you run a buy-back program to "get them all"? That's in quotes because if you think such a buy back program will get most "assault weapons", I think that's wishful thinking. It's also less likely to be politically viable. At most, the anti-gun establishment will be able to reenact something roughly akin to the 1994 ban, maybe expanding what it covers a bit, and even that would come at a very heavy political cost.
None of your proposals would probably stop another Lanza. Most of the people crazy enough to drive their kids crazy like this won't obey a federal mandate to turn in their guns.
What you call "comprehensive" gun control, would have to be a ban on semi-automatic rifles with detachable magazines, semi-auto handguns and revolvers, because all of those can be quickly reloaded. If it could be enforced, it might work, but there's no way to either collect them all or prevent new guns from being smuggled in (or stolen) without extensive 4th-amendment violations. Not to mention that it would require a constitutional amendment (or one of the pro-gun supreme court justices could be replaced with an anti-gun justice, I suppose).