I think it's wise to attack from underneath if you can to avoid having to refinish the deck. I had some rot around my deck fills that I was able to remove with various tools through the 1 1/2" holes in the deck. You could think about drilling some 1" holes underneath which would allow you to remove a 5 - 6" diameter circle of core. I found a long thin phillips screw driver bent at a 30 degree angle near the handle gave me a lot of reach. You could then patch the 1" holes pretty easily. You may be able to fill the void you created with thickened epoxy from the hole(s) in the deck above. Use your imagnation and try to avoid cutting/drilling the deck.
Another approach is using vacuum pressure to remove the moisture - you can pull from the hole in the deck where the moisture originally entered so no need to drill new holes. I have done this to lower the moisture level around my chain plates (wood was still solid) - went from 20% down to 10%. It takes some time and you need warmish weather but it definitely works. Check out this thread:
I have recently been following a couple of threads where wet deck core is being repaired by cutting off interior or exterior skin and full replacement of the core. Two years ago I thought that I was in for the same on my 1988 Catalina 30. I found a crack in the deck that was weeping brown...
forums.sailboatowners.com
Regarding the injectadeck expanding foam: I think this can work but I would try to get as much of the moisture and rotten core out first.