The hard stone did not float. I feel sure you are right, that a lot of people are discarding the hard stones without ever noticing them. Like you, I found the collander idea too gross, so I used a pair of disposable chopsticks and a sort of panning-for-gold procedure.
I missed the stone on the first search (even though it was fairly large) and only turned it up on a very careful second check.
Yes, the seeds came through loose, unattached to anything. Since I didn't get much in the way of soft stones this time, that part of the test also didn't pan out, so to speak.
I think flax seeds would be much better, since they will be easier to notice.