Thanks again for everyone's responses. I just heard back from Larry, and indeed he's being very helpful. Of course it's possible that the razor isn't honed properly, but he's saying it's far more likely that it's a technique issue. I believe it! One thing he suggested was doing an initial "beard reduction" pass where the blade is flat against the skin. I'm certainly willing to try it, but I'm wondering, is that the usual way the first pass goes? I can't remember that from any of the videos I've seen.
Also, my growth was really minimal this morning on my cheeks, so I didn't think I needed too much reduction as I was already working with very short stubble. But maybe I'm missing how that process works.
In any event, I'll give it another try tomorrow and also possibly try stropping on the oxide balsa strop Larry included in the kit, as he suggested.