Where to put one's best power cords??

Depends on equipment and cords. No definite general answer. Listen. I would start by putting the cord on the preamp first, then move upstream step by step. After that to power conditioner if you use one and then to power amps. Unless specifically designed for digital, transports and dacs, good heavy gauge cord should work well everywhere. Purist Dominus cord that I have works best everywhere ! I left it on the integrated unless making recording from vinyl to tape - then I put it on the phono stage. I record directly from phono, no tape-outs.

Some or most power cords need in fact more than 300 hours to reach their full potential, but yeah 300 hours should get you most of the way.
Shunyata power cords are widely considered among the best overall. I thought about getting one but then the Dominus came up. I could use couple of better cords, though, on the phono and PS Audio regenerator. But this would be expensive and not so easy, Custom Power Cord Top Guns that I have are quite good, so it would be at least $500-$600 each used, thinking either Purist or Shunyata.