I'm not a physicist, but wouldn't there also be an issue with the moon's gravitational attraction and/or the moon simply swatting the thing out of the sky if it's really going slowly enough to avoid shattering and/or burning up on earth re-entry? What I mean is, IF the hypothetical planetissimal was going slowly enough to sort of ease itself into the atmosphere wouldn't it be spending quite a bit of time crossing the moon's orbit? It would have to be coming in practically on the ecliptic at almost exactly the speed of earth's orbital velocity around the sun (say, a few meters per second closure rate) - especially if it was the consistency of a soft squishy ball of clay like LRP proposes. This would also imply that it had to do some really fancy ricocheting around the outer solar system to get into that vector in the first place...
Any mathematically/physics inclined people here care to try and calculate the three-body problem here?