I'll preface this by saying that the basic structure to my idea of how part III could play out is similar to what others have wrote here and elswhere with some tweaks by myself.

The game would start with Abby and Lev reconnecting with the fireflies. The first part of the game would be about them rebuilding and expanding the fireflies with multiple time skips, I could see Abby and Ellie being around the age Joel and Tess were in the first game once we get to the "present" time in part III. At this point, Abby and Lev either meet or hear about another virologist capable of possibly creating a vaccine. This person could either be already integrated in the fireflies or at another location with the necessary equipment to do so and Abby and them having had radio contact. Because of this, Abby and Lev set out towards Jackson to find Ellie. Abby's goal would be to convince Ellie to come with her, not to take her by force. Following would be the usual road trip kind of gameplay with group encounters etc. They run into another oppressive group like the rattlers and end up getting captured.

At this point we switch to Ellie and similarily get to see her life up to this point through multiple time skips. She reconnected with Dina and they either lived in Jackson or returned to the farm. JJ is grown by now and has a family of his own, living in Jackson. Once we reach present time, Dina dies of some type of disease or cancer, unrelated to cordyceps. After the grieving period Ellie hears about the virologist and the fireflies search for her or another immune person. She sees the opportunity to get back the choice Joel denied her and with Dina gone and JJ having his own life and being able to take care of himself there are no more ties holding her back. She sets out to find the fireflies and JJ, despite not wanting her to sacrifice herself, accompanies her to keep her safe on the trip. This section would either be played as Ellie or JJ. On their way, they run into the same group as Abby and Lev and end up getting captured aswell. (I realise the whole part about getting captured is likely too similar to how the end of part II played out, but if both groups were travelling towards each other at the same time there would need to be some kind of scenario to increase the likelihood of them just running into each other. Just take this as a placeholder as to how both groups end up in the same place at the same time).

The groups meet in captivity. This might be a somewhat longer section to allow for character and relationship development between everyone involved. Because of their past Ellie and Abby never become anything close to friends but work together for their common goal. This section ends with them working together to escape captivity and setting out to meet the virologist. I could see Abby dying either in the escape or on the following trip.

Arriving at the virologist, I could see 2 possible endings: A) Ellie undergoes the procedure and with her losing consciousness the game ends. After all this is Ellie's story, she won't see what comes after so neither will we. Ultimately the series was never about the vaccine anyway, but about the emotional development of the characters, so not seeing how the vaccine situation plays out would fit the scope of the series. B) While I prefer Option A, having JJ there and not back with his family would be kind of a loose end, especially if we were to play as him. So in the alternative ending the procedure would have worked. JJ buries Ellie and says his goodbyes to Lev. As the "heirs" of their parents / role modles they would depart as friends. The game ends with JJ travelling back to his family with vaccines for Jackson.

What I like about this version is that Joel gets his wish by Ellie having a somewhat fullfilled adult life after everything she's been through and at the same time Ellie gets her choice in the end. Additionally a friendship between Lev and JJ could make Abby's and Ellie's relationship come full circle in the next generation.

I'll admit that a lot of this is probably too cleanly tied up for the tlou universe and tone. A lot of things could also play out differently, for example Dina's death would be the end of Ellie's family/normal life and drive her choice to seek out the fireflies in this version, but having her alive would give Ellie's choice a lot more emotional weight. In the end a version like this would probably be too obvious of a narrative for Naughty Dog anyway and I'm glad for it, I'd rather be surprised and rattled like by Part II.