Now I have a method. I start with the original version, record the beat, derive the BPM, speed up the original version, derive the new BPM, then record the parts onto the click track. I've also learned to watch for pegging the meter in both the individual tracks and the mix, and how to copy and paste segments of multiple takes to get a "best of" take. I'm also learning the parts by slowing down the original version, then adapting the part as I speed it up to the speed I want. I'm also using my boredom intolerance and punk sensibility to trim all the unnecessary breaks and repeats and solos.
None of which I knew the first time I recorded and mixed Blue Bajou. I spent most of the demos learning how the tools work. This time it's personal.
More on the punk minimalism ethos: If you play it fast enough you don't need repeated lyrics or solos. The whole song's a solo. The Dead Kennedys explain it in "Pull My Strings":