I tore out the ice box top and lid which enabled me to access the shelves and plywood cover board. I never liked the way the shelves are designed. It is nearly impossible to reach anything one puts on the shelves. So I decided to tear out the shelves and the face board at the same time. I am very pleased that I did that for the conditions they were in are atrocious.
After that I stared the factory original fiberglass ice box liner for a long time. It is really well designed (this is a west coast Triton and the ice box is accessed from the top, different from the east coast Tritons) and executed. However, there is no way to add 4 inches of polyiso insulation material which I plan to do. There just is not enough space between the liner and the plywood bulkheads that surround it. At the best I can add two inches of insulation which is really insufficient based on everything I have read (Nigel, Don Casey, Tim...) After about half an hour I made up my mind to cut it out and build a new box based on the method Tim and Nathan described in detail on their website.
Cutting out the ice box liner was not as difficult as I thought although it did cost me a 4-1/2" cutoff wheel and couple of small Dremel cutoff wheels. After I yanked the two half pieces out of the box where it has been sitting in for over fourty years I felt victorious. I wish I had a camera to take some pictures of process.
I now konw how Nathan felt after he took out his ice box with Tim's help.

After I pulled out the liner I finally had the opptunity to see what Aero Marine used to insulate the ice box. They used 1" thick insulation material that is commonly used for houses, which in addition to being a poor insulation material for ice boxes is in a terrible shape after 40 plus years. What's more, the additional foam that I sprayed into the cavity couple of years ago using the can sprays through 1/4" holes drilled around the box barely made any difference. Most of it settled into the bottom and corners of the cavity. Even in those areas it is at most 2" thick.
Finally, there is a puddle of water accumulated at the bottom of the box. I guess the water in the ice box did not all drain into the bilge. The drainage hose is already hardened and brittle and the joint with the drain fitting had a crack in it.
I will be putting a proper ice box together over the next several weekends and expect that I will have many questions. The first questions I have now are (1) are two layers of 2" polyiso better than four layers of 1" polyiso? (2) How many sheets I need to buy? (3) What is the best tool to cut it? (4) Do I need to glue the layers together with epoxy?