Some great advice here — this is definitely a marker.
Just wanted to respond to Don's musings about the speed-up being from the tightening spiral of the record. Unless there's some arcane physics thing going on, I don't see how it could. The revolutions are the same (78, 45 or 33) from start to finish and the music is spread into the grooves evenly in the manufacture of the record — i.e., if a note lasts for one inch of the groove in the first cut, it would last the same one inch in the last cut. The only difference is that the spiral is tighter, but that doesn't shorten the transcribed note. Think straightening out the groove and you'll see what I mean. So if it goes on that way, it'll play back that way.
Clear as mud? Maybe somebody else can explain it better.