So glad the chaeto blob works for others. Of all the methods, this is actually the one that I used and that worked reliably for me multiple times.
my chaeto was full of amphipods as well. I feel it's likely important.
chaeto really doesn't put out much in terms of chemicals it exudes. every other algae puts out way more than it does. It is likely that chaeto brings its own bacterial community which may well disrupt the community the dinos relied on. These are the best theories I have on why it may work. Amphidinium just aren't bothered by that low level of shade.
This may seem weird but ought to be expected. Since we start with a dino bloom, the dinos exponentially grow until they run out of something. So once our dino bloom plateaus out, then we know something important has been depleted.
Then add Si to the mix. The diatoms can't have a big bloom because they likely need the same things the dinos have already depleted. But now there's more than one exponential grower on the block and any trickle of the scarce resource may now be taken up by diatoms, so the dinos don't get all of it.