In my opinion, you have minerals leaching off the encrustations, and likely not hte base metal of the coins. I don't think there are any bronze-oxides that are white.
In terms of DW soaks, DW is only effective because it causes ion migration from mineralized objects (like dirty coins) to the de-inonized fluid (the DW), thereby loosening crusties. DW should be changed daily, even when soaking for months, or it loses effectiveness.
It's possible the white stuff is also bacterial growth from leaving dirty water sitting for months... just saying.