Choose the first scene in the series, hide the objects you want to hide, select all of the scenes in your sequence, click the Update button in the Scenes tab, untick all of the boxes except the one for Hidden Objects. Then click on Update.
That’s pretty great, thanks!
It turns out that most of my problem is that I am using an excessively wide angle for viewing small interior spaces. Something that Sketchup is inherently bad at, because the wide angle cuts walls within the angle of view.
Any work-arounds for that?
Not so much. You’re dealling with clipping. Effectively you’re putting the camera in a position where some of the geometry is “in” the camera. Most likely in your case hiding the stuff makes the most sense. Best would be to use tags for controlling visibility of the groups and components instead of using Hide. Maybe section planes would be a workable solution, too.