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Hmm, apparently the problem was nothing to do with movement assuming a a framerate of 30 FPS like I thought. It was to do with floating points. (If you don't know, computers aren't very good at calculating decimal numbers. You could tell a computer to calculate 1 + 1 and it wouldn't be shocking for it to return 1.99823.) Apparently an optimization we were using took approximations too far, resulting in the bugged movement. We're no longer using that optimization.
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I am amused. Especially given that my own code fell in a heap this morning due to floating point comparisons.
It wasn't my fault. How was I to know that Python can't even copy a float to a new variable - with no arithmetic applied - and retain its binary form?!