I finally got past this problem by rolling my own audio recording software. I paste in the script, and the software highlights one sentence at a time. I tap a key to start recording that sentence. If I make a mistake or I'm not happy with how it sounded, one key press discards the audio and restarts the recording. When satisfied, one key press moves it to the next sentence.
When I'm done, I can download all of the recordings into one merged WAV, and I never have to hear any bad takes (it also trims 0.1 seconds from both ends of each sentence's audio so the key press noise is removed).
It's a little clunky, being home-grown and all, but it works great. Recording stuff is pretty easy now. I keep thinking about making it available to the public, but it's not yet polished enough for that.