Wow, you people here really seem to know what's going on. I wonder if I am indeed in too high a gear sometimes? I'll have to experiment more with that.
I'm using clips, which help with lifting on the upstroke, though I think that the muscles I'm using for that are tired, too. I'm riding a hybrid and will not be putting any serious consideration into getting a real road bike until next year, so I'll save the clipless purchase for then.
I think maybe I am trying to progress too quickly. I know that I'm getting impatient with my average speeds. I think I'll have to take things in stride and try to enjoy the riding more instead of engaging in all this relentless pushing (which has been fun, but the last thing I need is to push myself too far and ruin cycling for myself).