The one gypsum roof deck I worked on involved spot leak repairs. As I remember it, the proceedure we followed was:
1. We inspected the deck from below to locate suspect areas, as you noted, water damaged areas are generally quite visible.
2. We opened the roof from the topside, working from areas known to be solid. Don't forget your OSHA harnesses and hole protection!
3. We removed the damaged poured gypsum deck and panels (2'x4' if I remember correctly), but we left the bulb tees where we could, since they were still in good condition. However, many had to be cut out along with the deck, so in most instances it is cheeper to install new.
4. We placed new bulb tees, laid gypsum "form panels" in the bulb tees and then poured the new gypsum deck. We used a small grout pump to pump the gypsum to the roof deck.
5. The existing roofing membrane was then completely removed and a new roof membrane installed.
The key, if you do the job yourself, is finding the matching materials. There are specialty contractors that do this work and I'm sure you can find some names on the web.
Good luck.