Interesting, indeed. Twenty or so years ago, I knew a guy that melted his own shot from old used wheel weights that he got free from tire repair shops.
He did as you explained with the lead, but when time to batch up the shot loads, he also mixed in a proportional amount of solder that he also melted into a cup of water with a soldering iron.
He said the mixture of heavy lead shot with the lighter shot made from silver solder helped his patterns.
I don't know for sure, though, because I never shot any of his loads.
Sounds plausible.
There are some companies now that put light weight silica ballast in amongst the shot as a buffer. They say it helps the patterning.
But I surely am not an expert on shot making by any stretch of the imagination.
I too would also be very interested in the application side of this theory, if there is someone who might try it.