Jose, the process you've laid out sounds like exactly the right way to tackle this. For now though I've decided to take the "patch it up" approach instead. To fix it the way you describe I'd have to remove a plumbing vent and a roof vent that are either in or adjacent to the soft spot, and I'm afraid I just don't have the time to dig that deeply into it.
Instead I'm going to seal up all of the caulked seams with Eternabond Webseal. The bulk of the soft spot is in the 12" or so between the rear seam where the roof meets the rear fiberglass cap and the plumbing vent, so I'm going to reinforce that area with slightly overlapping layers of the Eternabond. Then in the spring I'll recoat the whole roof with Liquid Roof or something similar. My theory is that 1) the soft spot isn't that big, 2) it shouldn't get worse if I seal it up tight, and 3) if it does get worse I can always open 'er up sometime next summer and effect a more permanent repair. If it comes to that I'll follow your instructions to the letter.