In her videos, Elizabeth Zimmerman does Continental purling this way, if I recall correctly:
She comes down into the stitch with the right needle, then manipulates the right needle to point up and grab the working yarn, and then down again to pull it through the stitch. The left hand which holds the yarn barely moves.
Also, I think it's common (maybe even more common?) to use the index finger, not the middle finger as I do, to push the yarn down. I found this trickier, because the yarn is on the index finger, and it can loosen or change tension to move it. But apparently a lot of people do it this way.
There's also Norwegian Purling (video in Purling section), which also has the yarn in the left hand.
I think any method is awkward until you've practiced and modified it to feel natural for you.
Hope that helps!