How I understand Elrond's comments

It seems to me that we should approach Elrond's words through the lens of Gandalf's question: what shall we do with it? I don't read his words as random comments; there is a logical flow here, though it requires some assumptions, and I think it all intentionally leads to Bombadil.

To paraphrase:
"...What shall we do with it (the Ring)?"
"Well, obviously Saruman SHOULD be the one to answer that for us, expert as he is in these matters; grievous news that he has betrayed us. What then? Well, Frodo mentioned some strange things (boy, aren't hobbits stranger than we thought?!) like barrow-wights and the Old Forest; I too know of these things, and in Frodo's tale both of those items pointed to a potential answer to the problem of not having Saruman... Bombadil [implicitly referring to his "power" over the Ring ]. Shoot, maybe I should have told him to come. How about Bombadil as our first item of debate for potential solutions for the Ring?"

However, your comments in the class about Elrond "verifying" Frodo's tale, and connecting it to the "Tale" and setting up the choice of Frodo for the journey are a compelling understanding of Elrond's words as well.