If I understand you correctly, what you want is to be able to mix indirect dialogue with direct dialogue in order to give an impression of the experience of recollecting conversations, where most of the recollection is of generalized things said, but there are a few direct quotes sprinkled in. You want to have that effect, but achieve that effect in such a way that it's not as off-putting to your readers as it currently is.
In the example you gave, I think the problem I would have with it is that it doesn't feel like natural, actual, literal dialogue. I can't imagine anyone talking that way unless they were singing a song. It feels to me like this is probably either a poetic summary of the conversation (in which case, the person summarizing is the narrator and nothing should be in quotes), or it's a song/poem, in which case representing it as a snippet of normal dialogue doesn't feel right.
I don't have much context for your story so I don't know. Maybe your character Ted is a poet or bard or someone who likes to recite songs or poetry or something like that is going on. In that case, I would say you just need to make it clear that that's what is happening. Call out that that's what is happening explicitly ("And Ted sang..." or whatever) and also format the snippet as verse.
There's at least two main ways to format things as verse. One is to give it its own paragraph. It stands alone, has whitespace before and after, and is indented. The second is, you can do inline, which means you typically put / between things. So if that's what you want I would replace your -- with /.
If, however, you're saying that no, this is supposed to be an actual quote of real dialogue during a real conversation, not Ted quoting or composing a song or poem, but real dialogue...hard truth, but: if you have several readers telling you that this doesn't sound like real dialogue, then: maybe you need to get better at writing realistic-sounding dialogue.
I think there might be yet a third option. Maybe what you want to do is to write the whole description paragraph not as normal prose description but instead write the whole thing as a song. That would be a unique move but who knows, maybe that would play to your unique strengths as a writer.
Hope this helps.