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You solve one issue, and introduced another one.
Interlacing is a good way to ease printhead overheating. When printing 10101 in a row, you might got 5 black dot (11111) because the overheating.
By printing the same picture multiple times, each time printing part of it, overheating can be greatly controlled.
However, there is no way to control the movement of the paper. The mechanic part is, hmmm, not designed for this usage.
Fig 1 is the result, printed with density 1, while fig 2 is printed with density 0 without interlacing. And fig 3 is what the result should be in theory.