I have been following this since day one but only had time to reply now... First Congratulations on a rare experience and find. Regarding your decision to keep all cemented as you found it versus, separating the coins, allow me to help you decide. In the 80's a local salvor who dived the Florida Keys in the 50's & 60's offered to sell me one of two nice display pieces he had recovered from a wreck long ago--a wreck now in the underwater park. He had two pieces of nice white coral, the lightest had to weigh at least two pounds. Atop the smaller clump was two separate green/black silver face coins that dates to the late 1700-s-early 1800's. The larger piece had three separate face coins. Each coin on the two pieces were at least 75% exposed and it was left as he had found it--only think, he chiseled the coin encapsulated coral from larger pieces growing on and near the wreck. I can tell you in mid-80's, a mere $35.00 would have bought the large piece of coral with the three coins. I asked him and he agreed to sell it for that. However, I had only $20 in my wallet and he would accept cash only. Unfortunately, someone overheard me offer to buy it and that person whipped out the cash and got it immediately. I ran down to the bank to get more cash, so to buy the second piece. It was sold before I returned. I ended up buying from him a single blackened Spanish face coin for $20. I was upset with myself for several years after for not carrying more cash when I attended this symposium because that coral with the three face coins could have been mine to this day.
The two coral pieces with the coins were, clean, white, with green/black silver dollar coins. In other words, they were beautiful display pieces and should never be separated. However, what you have seems to be more of a concretion/coral mixture and is not clean and attractive--it appears rather gray in color. In fact, I have seen shallow coral just like that off Key Biscayne, Florida, all gray and blackish. The reason it appears as such is because on a nearby key is the Miami Sewage plant with an emergency outfall. All this sediment washes back on the beach and settles in and below the sand and on to the coral, it is filthy and unattractive and it stains the coral. I have gone their to hunt in the water and not enter when the ocean water smells like tell-tale sewage. In closing, I think you should compromise the decision. Have someone assist you in removing three or four coils from the bottom, and keep the remainder in clump form. I have seen much more attractive display pieces than what you have found. Nonetheless, you should photograph every angle and do an article in some US treasure magazine. PM me and I will suggest one.