First of all, it is an open question whether or not Ashton was permitted to rely on his memory and notes. Something was apparently said at a sidebar on this subject, but we don't know what. Personally, I would interpret an order sealing a document to mean that I could not tell anyone what the document said without court permission. However, (1) I have not researched Florida law on this issue (or Arizona law for that matter) and (2) if Ashton said that HHJP specifically gave him permission to use his memory and notes, I am inclined to believe him over Mason. Just my own inclination. But I haven't seen any direct source that Ashton said this.
Attorney notes about a deposition would never be sealed and in fact would never be in the court's possession. Certainly there is no question that Ashton could keep and use his own notes. The question is whether he could tell the rest of the world what happened in those depositions, based on his memory and/or notes. If this was, in fact, permitted by HHJP, I strongly doubt that there will be a hearing to find out whether Ashton used the deposition transcripts instead of his notes. As you say, it would be close to impossible to prove one way or the other.
My concern is that HHJP might have said something at the sidebar like, "You may use your memory and notes to communicate with your own expert / consultant/ etc. as needed to prepare for trial, but may not show the actual transcripts to those people." Pure speculation on my part, but I could imagine him saying something like this. If a judge said something like that to me, I sure would not assume I could use my memory and notes to communicate with persons not involved in trial prep about the contents of the sealed documents.
Again, we just don't have enough information at this point to know the answer.