Ok, so the thing that made my DVMs start working again was adding the relays tag. Which is weird, because adding that tag really shouldn't do anything at all — if you choose the wrong relays in the first place, the DVM isn't going to pick your request up, regardless of what you put in the relays tag. Just put the response back on the relay where the request was found right?
As a sidenote, I've noticed that a lot of the new primal DVMs don't have kind 10002's, so it's impossible to know where to look for them (apart from hardcoding primal's relay).