The most recent time involves a DVD ripped using Cinematize to DV-NTSC 29.97 with a sample rate of 48k.
I tried converting this to 44.1k, but this didn’t change anything.
Original file from Cinematize plays back fine in Quicktime, but when imported into FCP the previously stated problem occurs.
Exporting out a DV Stream file from Quicktime Pro solves the problem regardless of sample rate (I have tried 32k, 44.1k, and 48k).