Re: to glass or to marine polyurethane
...I fixed mine by cutting back to good wood and spanning the whole thing covering the whole thing with 5 coats of enamel paint and then covering the whole thing with a single piece of aluminum. You can get old highway signs at the scrap yard pretty cheap. I just beveled the edges of mine, drilled countersunk holes and covered the entire floor with AL. Something like that might or might not be applicable to your situation. Mine has been fine ever since though I do keep it out of the rain.
What you describe here is not a "repair", but a patch. This can work for a time, but without removing all the wet and rotted wood will not last. Using aluminum signs and scrap to cover the wood isn't a solution either.
...It just seems that ripping the whole deck up to fix one spot when the rest is otherwise completely sound can mean a lot of unnecessary work....
The problem is that the one spot is likely the tip of the iceberg. Taking core samples of the wood floor can answer the question, but judging by the pictures the damage is going to be pretty widespread. If core samples show that surrounding wood is not wet or rotted, the cutting out the wet/rotted sections and replacing with new wood glassed in is OK, but again my bet would be that the damaged area is widespread enough that I would want to replace the whole thing.
As I said before, I did a patch job on my Sea Ray to get through the 2008 season, but will be replacing the whole floor this winter. The soft spot on my floor was also only about 1 foot diameter, but I replaced about a 3' x 4' piece of floor and I was still not to dry wood. I got to wood that did not appear rotted yet, just wet, but I know the rot would eventually be there and the only way to get rid of it is to replace a much larger portion of the floor. Large enough that I decided it was worth it to just replace all the floor/stringers.
1955, I think your decision is a good one as you will know when done that you have a good solid boat. Good luck.