Greetings: I also have a 1983 205 Overnighter Gulfstream (I/O) which I purchased in 2009. When I got the boat I knew that the floors were soft near the transom. After using the boat for two years I did a bit of investigating and discovered, with the help of a surveyor, that my transom was shot too. This lead to a two year rebuild which I did myself. At that time when I pull the fuel tank to get access to the stringers I discovered that a previous owner have added a plywood floor over the original floor which supported the seats. A black carpet had been added on top to hide the work. The carpet contributed to rot in the bulk head and the cabin doors, but the extent was not too bad when I discovered the problem.
To solve my problem with the transom and the floors, I cut out the rear inner liner and removed it. This gave me access to the floors and the entire transom area when the engine was removed. What I found was that the transom was completely rotten and was dangerously unsafe. Also the aft two feet of the stringer were rotten and the corner braces which sit on the stringers and form a triangle with the transom and the sides of the hull and support the batteries and other aft gear were also shot. Once I had access to the area, removal and replacement was not too difficult. I used marine grade ply rather than the construction grade these boats were built with and sistered the new stringers to the sound old ones further forward. All this was glassed in place, of course. I have a good set of photos to show the work progress if that would help.
On the positive side, the older Overnighters with the lapstrake construction are very good boats and well worth the effort to restore. They are much stronger that the flat sided newer boats due the angle support provided by all the lapstrakes. Apparently the reason Grady went away from this build is that they were have trouble getting the hull mold to release without chipping along the lapstrakes. The stepped hulls are easy to buff up with a soft power buffer and a bit of light grit polishing compound.
Going back to the question of the base under the seats,,,,,,,,,In my case the old floor was cut out and I just have a piece of 3/4" ply overtop. I crawled in to inspect the area along the centre of the boat (where the gas tank goes) and could only see the new ply floor. What I can tell you is that the aft floors in the area aft of the seats is made of 6" square of 1/2"plywood (much like a par-kay floor) which is sandwiched between two sheets of fibreglass. It is common for water to get into this area and rot out the entire floor. When I removed the inner liner and turned it over, the area was easy to work on, but it is very difficult to access if the liner is left in the boat.
So while this might not be what you wanted to hear, it does prove some solutions for the handy boat owner. From my experience, I would certainly have a surveyor check the boat out and then use him to help you develop a plan to evaluate the problem further. In my case I was able to find a experienced fiberglasser who guided me along so that went the time came to cut out the liner and then replace it, he was able to step in and bandage the wounds sucessfully.
Cheers, BCBryan.