I don't think a planet sized object can do it; both Earth and the object don't just melt, too much of it actually vaporizes (Not in the Star Trek sense, but the scientific sense; being heated beyond the liquid state (melting), beyond boiling, to the gaseous state: vapor; like steam for water).
The amount of convection and random movement in this hot state will make it impossible to separate the components of the striking object and the parts of the Earth's crust and mantle that vaporized. Some of it settles back on Earth, some orbits the Earth.
I do think it is possible, if your mass and distance and orbital periods are all consistent, for the moon to be of a different mass and in a different orbit around the Earth.
Your better bet, to increase the heavy metals on Earth, would be a period of heavy bombardment by smaller meteoric impacts that do NOT penetrate too deeply. The Chicxulub meteor that wiped out most dinosaurs 65M years ago left a noticeable planet-wide layer of iridium behind, but the impact crater itself was only 93 miles wide and 12 miles deep.
Now supernova are required to produce heavy metals like gold and palladium, and when they do, they produce them in massive quantities and spray them into the universe. It is plausible science that some stray rocks made entirely of such metals from a nearby supernova could impact a planet like earth, vaporize like the Chicxulub meteor, and spread those metals uniformly on the Earth. You could put the timeline anywhere, even billions of years in the past.
In the link, you can read about the Multiple Impact Theory; many other impact craters occurred around the world at nearly the same time as Chicxulub. So another possible scenario is that a heavy metal asteroid was gravitationally captured by the sun and was in its own unusual orbit as a result. Since it wasn't in sync or in the plane with the rest of the debris around the sun, eventually a collision with some other large rock broke it up and the pieces ended up on a collision course with Earth; but (like the Shoemaker Levy asteroid) broken up into a 'string of pearls' of various sizes, none of them particularly catastrophic, that basically sprayed the Earth with heavy metals over the course of a few years. That would lead to a less uniform distribution of heavy metals; you'd have regions tens or hundreds of miles with high concentrations, while other regions had lower concentrations. Of course then you also have continental drift, earthquakes and other forms of mixing so the regions would not be just circles on the map; and water and rivers could move and even further concentrate the heavy metals far from their deposit areas. That is why we pan for gold in streams and rivers.
I'd suggest some kind of bombardment like this. This would better explain a differential between the two bodies. The bombardment could occur on the planet (like Chicxulub) or on the moon: From its cratered appearance it has clearly taken some major hits for us many times in the past.