The cage won’t shift regardless of which cog the chain is on while riding. It’s an old Sugino AT crankset and rings (on an 85 Schwinn Voyageur SP, so all older parts), so there could be wear. I’m not near the bike until tomorrow afternoon, but wear could certainly be a factor.
It’s seeming like I should start with letting out the low limit screw. There’s still room so I’ll start there and report back tomorrow.