Looks like you've done all I would do. Do expect to get some flak from folks about using bleach as it is common for that when mentioned. Too many who don't understand , so they are afraid of it! I do lots of wood and bleach is simply tap water with much more chlorine, so the chlorine gasses off if we give it a chance. Let it dry until the smell is gone and that means all the chlorine has gassed off and when it stops getting in your nose!
How much loose wood to remove, kind of depends on how much you feel it will be a problem to chase down if it does come loose and float around in the tank. Looks good enough from here.
For holding down, I like screwing tile to the bottom so that I can better choose the angle, etc. but that does need a drill and masonry bit to drill the holes. Other times a few rocks on top will do nicely to hold it.
Nice wood should never be left on the shore to rot!