As mentioned above, I removed the screen "bulb" from the glass stem and turned the mouthpiece upside down. That didn't work out so well after all. Too much herb still got sucked up even though the stem wasn't sticking as far down towards it.
Instead, I've cut a small disc out of a heavier stainless steel screen and dropped it in flat over the herb. It is slightly smaller than the herb hole and so will dump out easily, but not nearly small enough to be sucked up through the stem (a possible though unlikely danger with the stock screen). I also turned the mouthpiece right side up again, but left the screen bulb out of the stem since I am using the external screen. One test draw seemed good - plenty of airflow and no herb coming up.
Edit: After a few more pulls, I can say this is how I think I will be using it. You do have to exercise more breath control because of the freer airflow, otherwise you can easily swamp the chamber with too much cool air. Also, one time I sucked too hard and turned the screen on its side allowing a little herb to come up, but I can control that. This is of course very similar to VaporEyes method, but I prefer not to friction fit a screen and have to pull it out when done, and it should be easier to clean overall.