If you have to cut the carpet to fix the soft spot, you most likely will have to pull some/all of it up; I don't think you can cut out a patch and replace it, without it looking like heck and fraying. Assuming you have to replace some of the carpet, cut a hole in the deck larger than the soft spot with a circular saw set for 1/2". If that doesn't cut thru it, increase the depth by 1/8" and repeat until you cut deep enough to get thru the decking material.
Then pry up the piece, and inspect the foam and any structure below. You most likely will need to cut out some foam - it's probably wet and/or compromised anyway from whatever has been causing the soft spot. As you remove foam, you should expose one or more stringers or bulkheads. Drill a 1/4" into those about 1" from the hull. (You also should do this on the sides of the motor mounts and along the walls of a ski locker, if you have one. Those ski locker walls are usually stringers.)
If the shavings come out dry and light colored, fill the holes with 3m 5200 sealant, get some Great Stuff foam to fill the hole and patch your deck. Then go buy your lottery ticket.
If the shavings come out wet and/or dark, you have structural issues that will need to be explored further.
None of us are saying this to be mean or gloomy. Many of us have been in your shoes: we found a problem, looked for ways to deny it was as bad as we feared, but eventually we learned that our boats had problems. If often starts with one soft spot or a screw that turns and doesn't seem to bite into wood anymore. It would be great if you don't find yourself in that position. But it would also be a little surprising...
Good luck and let us know what you find.
