I've left most of the posts of members answering in place because I'm lost on this one too. I've never had such an experiance nor heard of anyone else having it. So I'll give my suggestions and ask that you post whatever solves your problem so the world can avoid the misery you've gone through.
Re: The overheated alloy suggestion.-If you are using a Lee pot in a breezy area, (which is wise to avoide fumes) the breeze WILL cool the thermostate housing enough that the thermostate fails to sense pot temperature. I've seen the alloy glowing red hot in dim light with LEE pots in a breezy area, and when placed in front of an exaust fan. All the other melters I've seen or used, put their thermostate senser inside the pot housing and sense temperature more accurately. - If you don't have a thermometer, you can see a dull red glow at about 900 deg F if the pot is in a dark area, but it won't be visible in good light. Since 900 is a safe upper end temperature for most alloys, a dark test will reveal whether your pot is overheating the alloy excessively. Excessively meaning that oxidation and excess fumes will be given off. Far better to work at a temperature only a little above melt temperature of the alloy of interest.
Re: Excess Arsenic. High levels of arsenic are used in shot to make it form rounder balls as it falls from shot towers. I've read of it causing cracks in bullets, but never causing crumbling.
Re: Cooling ingots in water while too hot. - I've never had a problem with any alloys I've used in this respect. Even pouring molten lead into water leaves firm balls and pieces. (Shot is poured at the lowest possible temperature.)
My suggestion is that too much arsenic, coupled with a Lee pot on a breezy porch, and perhaps going away to wait for the shot to melt down, but not returning soon enough. (This is a common ailement of mine!) My guess being that long exposure to excessive heat causes the problem.
When using shot for bullets it is normally considered wise to use it primarily as a source of arsenic, in quantities of about 10% shot, which supplies adaquate arsenic for good heat treatability of the alloy. Arsenic vaporizes off readily at high temperatures and is extreemly toxic in gaseous form. Always use good ventilation when melting lead of any kind. If you can smell it when you walk into the casting area after a short absense, you don't have enough ventilation.