So I'm going to write up the approach that has been working well for me in terms of generating significant amounts of artifact power for alts with what seems to be a minimum of effort. While I'm putting this out there, I also fully acknowledge that this approach will definitely be impacted by the release of Patch 7.1.5, which is right around the corner, although in general, the changes in that patch may actually make this method slightly easier to execute on.
So here's what I do:
Once you hit level 110, don't do much of anything other than the regular artifact knowledge research every couple of days. You can certainly finish up the class order hall campaign if you want to, although there are also benefits to waiting on that.
The one thing that I do make sure to do is the Nighfallen emissary quests every time that they come up. You can do Kirin Tor emissary quests as well, but frankly those have gotten to be enough of a pain in the butt, that I can certainly understand passing on them. Note that without unlocking most of the Suramar story line, it'll likely take you more than one day to do the Nightfallen emissary quest because of the limitations on the world quests available. The good news is that means it'll be a bare minimum of time each day.
The rest of the process starts once your artifact knowledge gets to something over 20 which takes a little over 3 months at current rates, but will become significant faster once 7.1.5 drops and you have the ability to "buy" alts up to artifact knowledge 20 instantly.
At that point, go out and do the the full Suramar story line. If you did the full 3 month wait approach, while doing the regular Nightfallen emissary quests, you should have enough rep with Nightfallen to knock out the entire thing. If not, it's going to take you quite a bit longer. At level 25 of Artifact Knowledge, the Suramar story line is going to earn you enough artifact power to fill all 35 traits on your weapon. And it's a hell of a good story in the process.