Whatever you do to wash it, remember that Pb is toxic and can be absorbed through the skin.
To me, it's not worth messing with. Lead has doubled... this is not good news and does increase the price of shooting. But... I only shoot 10,000 targets a year. That's 25 bags of shot, and the increase in price over the last year stands to cost me about $500/year.
Significant, but not to the point that I'm going to give up my primary method of escape from the nutty modern world. Many things cost much more than shooting, even if you do it in moderate volume.
I'd actually get less enjoyment out of shooting if I had to spend what little free time I have reclaiming shot.
A bigger problem by far is the cost of travel to go shooting.
