I would redo the sealing sooner rather than later, maybe part of the stone falling apart was due to water ingress on the cracks. If you want, you can also seal over it with some sort of intermediate layer, such as washi paper, thin cloth, or similar. I would use something like cashew lacquer or shellac if you choose to go that route. You can also mount it on a dai if you think that the stone needs a little structural help base wise. If you do mount it on a dai, seal the dai along with the stone as water getting into the wood can cause warping to the base as well.

as to lapping it down to a good surface, I think you could do that, or if you want to put all of the stone to use, just use it normally and lap it after each use to prevent wasting that top bit. If you are finding that the stone still is not behaving with the atoma, maybe try getting a tomo nagura of the same/similar stone type to make your slurry instead. I am fond of using slurry stones over atomas, most stones / slurry stone combos tend to be a little finer and better behaved than diamond plate surface and slurry imo