Well, Quintus Curtius pointed me in a new direction, whereupon I felt mildly dumbfounded that I hadn't thought of it or seen it before.
Basically - all you need is airflow. And salt. Oh, and to keep it away from pets not only to not having it get eaten, but if your dog sheds (huskies, retrievers, etc...).
Here's a few links:
This is the closest I've found to what Quintus was talking about - certainly closer than the "box fan" method:
The box fan method per Alton Brown is explained here: but I don't like it for two reasons - I don't like picking paper/filter material out of my meat, and given what filters cost these days, it's not much of a cost savings. It does tend to deal with pet hair / environmental debris issues though.
More information on meat drying is here: http://www.fao.org/docrep/010/ai407e/AI407E18.htm
So why is it safe?
Salt is a preservative. As long as the meat dries fast enough, moisture isn't trapped in the meat, and there's nowhere for bacteria to grow. And you don't need heat - moving air is more than enough. You'll note dehydrators you can buy, which are cheaper than they used to be but still take up a lot of kitchen storage space compared to a couple cookie cooling racks, all have fans. And I've already got fans that can be repurposed for a few hours at a time.
Incidentally, I found Salt: A History to be an interesting book, though I don't recall any jerky recipes.
So racks that expose all sides of the meat to moving air, and keeping it away from critters and people that will eat it or get stuff on it. And getting enough salt in it to preserve it.
I've only tried once so far in a small batch. The thinner pieces were completely dry. I wasn't in a position to leave it out overnight so I decided to try what I had anyway despite the thicker pieces not being dried through after 4+ hours. it was delicious, I'm still feeling great, and next time I'll make sure I have the time or means to leave it out longer. It certainly, even in the thinner, drier pieces, was far more tender than most store jerky.