It's comforting to know that the problem may not be caused by fast-travelling! I don't do it often, but jeez, sometimes the nearest world exit is about five minutes away, and it's a little frustrating. What if there are bears on the way? And more bears? And what if the bears bring their friends?
Copying/pasting the abridged version: re: sound/banter, etc, I briefly did some experimenting on the Storm Coast. (I think my journal was clear, and I zoned into the area properly, if it helps.) I made sure I wouldn't have any trigger problems (combat overriding banter, triggering quests, no pinging, etc). For half-an-hour I did nothing but run up and down the beach closest to the main camp (around where you get Bull) to see what the 'natural' sound trigger states are. It probably took less than a minute to get from one end of the beach to the other. Riveting stuff!
As far I could see, for that thirty minutes or so of not interacting with the world (the game had nothing to do but trigger sound/banter/etc), it worked entirely as intended. Musical cues triggered about one/two minutes consistently - I think there may have been five/six different cues. (I think I heard two cues I'd never heard before.) I don't know if there's a musical trigger point that happens to be at the one end of the beach with the autosave trigger, or if it's coincidental, but it was extremely consistent.
I think I went about eight minutes without banter, then had a Dorian/Varric, a few minutes later, Dorian/Solas. (I'm sorry to say it didn't sound like the first time they've talked, either, so I'm not sure if banter is firing that I haven't been hearing.) They wouldn't talk again, but a few minutes later I must have crossed the Let's Have Your Party Member Comment on the Scenery/Weather trigger point that seems to be mid-way across the beach, and Dorian made a comment instead of triggering any party banter. (He'd also made a different one on the same spot when I'd first arrived to the Storm Coast, I'm assuming the spot isn't coincidental.) I know some people were theorising that the environmental/situational comments of the party were still considered as banter by the game, and I wonder if they're right. It wasn't like it was the first time Dorian had crossed that trigger point - twenty times or so before that - and it prioritised him talking about the weather, rather than having the party members chat. (There's probably some poor pained Bioware programmer going, 'damnit, that's not how it works'!)
Heh, this isn't a particularly useful post as it isn't a fix, and people have probably done this, but I thought it might be an interesting gauge for people with sound issues. As far as I could see, for that thirty minutes where the game had to do the bare minimum, the sound was working as intended. (I've had a lot of problems with banter/music in the Storm Coast before.) If you're having music problems and want to experiment, clear the nearest beach on the Storm Coast of enemies, and have a leisurely stroll with your BFFs. It'd be interesting to have the sound not working as you enter, and clearing the journal mid-jog or something to see if it helps. I'd be curious to try other areas as well, especially ones that seem to have more sound issues, ie. eternally silent Western Approach, etc. Just have to find a decent stretch of area where you can't be interrupted by anything - ie. fights, shards, quests, new area triggers, whatever.