I've done a total of 20 roasts with my popcorn popper, but nonetheless I have a theory worked out, which I'm sure I don't need to tell you should be taken with a grain of salt.

My popper is a $20 Toastmaster 6203 unmodified except for discarding the plastic top and using a $4 glass lantern chimney instead to keep beans from popping out. I don't have a thermometer.

Theory: Without special measures, a popper will roast too fast at the start and too slow at the end, so we need to correct for those tendencies. One way to regulate the roast is by switching the popper off and on.

Method:

Use somewhat more beans than the popper can move (you're going to help out by stirring with a wooden spoon). 100 grams works for me.

• A. Extending the early part of the roast. (early = up to the end of first crack)
  No warm up.
  Duty cycle: 30s on and 30s off. (Use around eight cycles, i.e. eight minutes.)
  No cover (except as needed to keep beans from popping out).
  Stir constantly with wooden spoon.
  
• B. Stretching the middle of the roast. (middle = between first crack and second crack)
  Duty cycle: 45s on and 15s off. (Use around three cycles, i.e. three minutes.)
  Use chimney uncovered when on.
  Stir with wooden spoon when off.
  
• C. Speeding up the last part of the roast. (last = from second crack to the end)
  Duty cycle: Always on.
  Use chimney partially covered.
  No stir.
  

Does that sound as though it might work?

I don't think duty cycling the roaster after the first crack starts is a good idea;

May I infer that duty cycling before the first crack could work?

I am experimenting, and I think perhaps the duty cycling has made for some improvement. But I'm not good at tasting yet, so it's hard for me to tell. I just tried a roast I did with my popper this morning that took 14:15 with first crack delayed to 8:30 by duty cycling, and it tasted good to me. I'll cut out the cycling after first crack and see how that goes.