Cardboard is free and the wedges cost money, but on a wet shower wall that cardboard soaks up water and swells. Pull it fast or you'll be chipping it out with a razor.

The part about "one small doubt they could not explain away" is the whole ballgame. In my experience the sign that gets brushed off most is the little rule that only applies to one person, like the leader gets to interrupt people but you get scolded for it. Everyone else waves it off as "that's just how he is" and moves on, and that double standard is usually the first crack. Write down the small stuff when it bugs you, date it, and read it back a month later. The pattern shows up fast when it's on paper instead of bouncing around your head.

Did the supply house guy tell you to use regular painters tape or the good stuff? Because that's where most guys mess up, cheap tape pops as soon as the heat hits the plastic and then you're wearing the soot. If you tape the poly down with actual foil tape around the whole edge and leave a slit at the bottom for a shop vac hose, it holds fine and most of the junk drops straight down instead of onto her carpet.