During last week’s canning workshop, I learned that all along I had been using my jar lifter wrong! Basically, I’d been using it backwards – using the black roller handles to grip the jars… which was always a bit precarious in hindsight. Here’s the way I was using it:

And here’s the proper way to use it:

It makes sense to use it this way, because the red parts grip better, so there’s less chance to drop the jar. And they are curved to better fit the jars. I’m going to use my jar lifters properly this year, which I expect will make the process quite a bit easier.
And as far as the confusion as to which side is the handle and which is the gripper, I’ve learned that I am not alone in this respect… many thanks to AJ for setting me straight.