I’d be inclined to say “I did do my homework, but the dog ate it”, but then I’m from the South Wales borders! 
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My brother first heard this in the context of a radio news report about “shoot-to-kill” allegations in Northern Ireland - a witness said the people were “after going through the checkpoint”: my brother thought it meant they were trying to get through without stopping, rather than that they were shot when they had already gone through.
To me, both of them are ungrammatical - I’d say I did it, but the dog ate it. However, I offered you both, because I felt that putting a time when the dog ate it (simple past, over and - unfortunately - done with) made it feel somehow even more clear-cut, so I wondered if it made a difference to you.
And if I’m asking for your feeling about something (rather than what the Standard English is/should be) then there’s no reason on Earth why it should necessarily be consistent - not that the Standard is, anyway!
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