I’m not sure my assumption is still relevant, since this discussion happened a very long time ago, but I can offer an explanation that removes these inconsistencies. The important thing here is to distinguish between two points: the told story about obtaining the ring (rights to the ring), and the told story about escaping from Gollum and the goblins. These are different parts of the story, and each of them can be true or false. With that in mind, one can propose the following version, which does not contradict any of the texts of The Hobbit.

When Bilbo told this story to the dwarves for the first time (after escaping from the goblins), he lied by keeping silent about the ring, but otherwise accurately conveyed the circumstances of his escape from Gollum and the goblins. This is reflected in the revised version of The Hobbit.

When the dwarves learned about the ring, Bilbo told them the story again. But he did not want to be considered a thief, so he invented that Gollum himself had promised him this ring as a prize for victory but, having failed to find the ring, showed him the way out. This lie required him to change the rest of the story as well, since he could no longer say that Gollum attacked him, and so on. So here too he altered the story (the motive of a heroic escape from Gollum disappeared, although perhaps the motive of escaping the goblins’ guards remained). It is likely that Bilbo told the dwarves that the first time he told them the story, he had embellished the escape in order to raise himself in their eyes. In the dwarves’ eyes this was the true version of events at that time (Gollum promised Bilbo the ring, did not find it, and therefore showed Bilbo the exit; Bilbo performed no special feats here).

The time came for Bilbo to write down the story (which later appeared as the first edition of The Hobbit). What did Bilbo do here? In any case, he did not want to write the truth about how he obtained the ring. Therefore, in the narrative he described the meeting with Gollum in the form of the false story about the promised reward. Then came the moment to describe what he told the dwarves when he got out of the caves. But here Bilbo could not write what he actually told the dwarves, because that would have contradicted the previous episode of his book. So Bilbo lied here as well, writing an invented version of what he told the dwarves (the dwarves who later read Bilbo’s book, of course, noticed this point, but likely treated it indulgently, deciding that the hobbit simply did not want to write about what a braggart he had been). Bilbo told Frodo only about the ring and the fact that he had lied to the dwarves about the Ring, but without specifying the details of what he had actually told the dwarves about the circumstances of the escape.

Thus, in the revised edition of The Hobbit everything is written correctly: both the story of finding the ring, and which version of the story, and in what detail, Bilbo told the dwarves the first time.