One big thing that I try to consider is giving the scene an emotional purpose, in addition to its informative purpose.
I really liked something I read in Ryan North's Back to the Future analysis blog (which I actually super recommend (EDIT: I went back and read the whole blog again b/c it's great and here's the entry I was thinking of)) where the characters had to introduce themselves to each other. It's small, but a boring bit of talking by definition -- you already know these characters' names -- but it's also required or else it's weird. He commented on one version of the exchange that emphasised the awkwardness of these characters meeting each other. That's good, he said, because you're getting something else out of the scene -- any time you have boring words that need to happen, try to at least get a character moment out of it. I think that's really good advice!
My comic opens on exposition -- Sev explaining how magic works -- but it's also a chance for us to meet this ridiculous guy talking about his latest "great idea" while his best friend watches with the kind of dubious amusement that implies she's seen a million of these stunts, and they never go well. I wanted the conversation to be just as much about who these characters are and how they feel about each other as it is about the information you're getting.
I feel like this applies even if you're showing flashback visuals or something. I tried flashback visuals to attempt to make both of Jonan's monologues interesting, but I think it worked on the first one much better than the second, because the second is literally just an illustration of what he's saying -- it's honestly kinda redundant and doesn't give us anything other than information. Whereas the first one, in addition to telling us what happened, also shows us that Jonan's version of the story doesn't quite match what happened, which automatically tells us a lot about Jonan himself. There's a secondary emotional purpose there that you're picking up on that makes it way more interesting.
So I do my best to approach all "infodump" scenes that way -- make it a chance to learn something about the characters. Sometimes that's visual -- just seeing how the characters respond to it, with body language and expression -- and sometimes that's a storytelling choice, putting info in a position where it can be argued over or bring two characters closer together or show us something unexpected about the guy who knows the info.