Are you sure that noggins will take the bounce out of the floor, I would have thought that once the floorboards are fixed to the top of the joists this would stop sideways movement, and if the joists are flexing vertically then neither noggins nor herringbone would stop this. I reckon that the best way to stop the bounce would be to fix extra timber down the side of the joists. If it can't be fitted right to the ends then fit them as long as possible.
I wouldn't have thought that small notches out of an 8" x 2" would have weakened them to any great extent.
I wouldn't have thought that small notches out of an 8" x 2" would have weakened them to any great extent.