It turns out there's a script/executable that can do exactly this. I'll run it once I'm home and then proofread/format it in some fashion depending on what the dump looks like. Thanks, Python!
Beholde, yon texte dumppe! According to Word it's roughly 161,000 words. I have no idea how long that is relative to canon episodes (nor is it done yet), but it'd make a fairly longish book. Yeesh. Note that most formatting is killed, including colored text, so things like the dream are an incomprehensible mess. Have fun with that.