Another data point on applying for STW after booking. I have an upcoming planned trip where the outbound is US city 1 -> US city 2 -> International destination city. When booking this, there was no ZN availability on leg 1, and ZN=6 on leg 2. If I tried to book the flight with PP upgrades enabled, it bumped me up to a higher fare class *and* didn't let me apply STW at all on the outbound I wanted (it did on another more convoluted option with multiple domestic connections where there was ZN space). After booking, I was able to apply STW to the second leg no problem, and waitlist on the first leg.

From everything I had read on this thread (and elsewhere) ahead of time, that was my understanding of how things *should* work, so I was pleased that they actually did!