Long thread is long, so I didn't read everything and might repeat something that already has been said, but here are my two coppers:
Storywise, it would be difficult to make a BG3. Here are a bunch of ideas:
Direct continuity. Idealy you would either play as a newborn god and face a story based on this or you go on a new adventure. This comes with a bunch of problems though, because you would either have to make two (or three) entirely different stories, depending on the ending you got. To prevent this, God-Charname could be stripped of his/ her godliness in the beginning or Mortal-Charname could be promoted to a god/ godlike status anyway, due to story reasons (I see a lot of delicious conflict with Cyric stirring up here ~). Or a "canon" ending for ToB would have to be chosen, such as was the case with BG1 to BG2 (aka, good-ish Charname with Minsc, Dynaheir, Imoen, Khalid and Jaheira), which I wouldn't like :/
The new Protagonist. The new Protagonist could be a child of Charname and one of the romantic interests from BG2 (EE). Idealy you could choose in the beginning who the mother/ father is and get a different origin-story alá DA:O. This way the ending of ToB does not matter in the bigger picture. An additional origin-story could be added where Charname never had a child and someone else is the parent, one or two old companions for example (I don't know, Keldorn and his wife, maybe).
The prequel. You play as one of Gorion's old friends and companions. This way it doesn't matter what happened in the other games. We could see the corruption of Ariana, Gorion's encounter with Firkraag and a whole lot of other things. The big finale could be the storm on Bhaal's temple and the rescue of Charname and the other children. We could also learn who Imoen's and Sarevok's mothers where. Imagine the possibilities!
Well, that's all I got for the moment.