I hear you. Not knowing your root cause is tough. Keep looking for a cause with whatever means are possible.
I have no idea how to deal with sufficants, from what I read sufficants rinse well. That's their purpose.
Isn't the sufficant (in water softner) that was in your system made for human consumption?
Here is something I tried when I was worried about Copper Still stuck in my Pile of Rocks.
Might help you lessen the worry about keeping rocks.
Take out one large rock or a few that fit into a bucket. Fill it with new Water.
Let rock soak it for a while, to run the leach test on a small scale.
Add a senstive invert at some point to that water.
I know you don't want to kill creatures. Certainly not fish.
Killing a Small snail to save many other creatures isn't too bad (It may live, or just slowly fade [fall alseep]). How many snails get horribly killed by hermits.
I did the same when I had a suspicion about a cracked Chineese Gyre. Place it in small amount of new salt water ,and after a few days tested the water. It showed copper. I threw out the pump.
Was it your salt? You said new bucket. Look up any recalls from Manufacterer.
Guess what wiped out my Tank. It was Kent Carbon. Brand new pail.
I used it one night. Next morning my tank was melting corals.
I didn't know what was the contaminant. So I wanted to clean up the systems. And I added more CARBON.
That finished off my tank even more. Clam had one last cough, and then vapourized.
I kept doing all kind of things going insane for weeks.
Then Few weeks later, at Fish Store I see a Sign. Kent Carbon Recall. Had Copper in it. When they mined the coal, they hit a copper vein. Quality control didn't pick it up.
After I gave Kent the Serial # of my carbon.....Kent took take of me, but the journey was a nighmare.
Believe it or not. THe leather Survived, so did the trumpets, and Nothing but skeleton left Frogspawn.
WISH THE FRIGGIN GREEN Palys got wiped out for good, but they are still around invading the tank.
All those Copper Contaminated rocks are still with me. No issues, and people say copper sticks around a long time.
Not months, but couple years for corals to fully make it back.
Same original Trumpets below. Same Frogspawn (actually pruned and sold a few times)
The leather eventually outgrew the tank and I sold it.
What I'm saying. Is keep the rocks if you like them. If it's a lot of rock like I had.
I'm glad I did, since I collected special pieces over many years like you did.
Leathers are like shoe leather. Tough. Yours will do fine in same salinity water. Just add a heater, airstone.
The decision to keep the rocks is something you have to get feedback more from other experts.
I wondered for a long while if it was the right decision for me.
100% peace of mind would obviously be to not keep rocks. Tough trade off.
Maybe keep the rocks and scrap the sand. Or really rinse sand (easier then rocks). Sand is a easy replace, not rocks.
All the best. I will tag along and hope the best for you.