You say your cats won't go near Yesterday's News: have you tried a long-term, graduate transition? They won't know that those pellets are for unless you mix them in, gradually, with your old litter.
I, too was looking for dust-free litters for my asthmatic cat (even though my vet told me it was not particularly likely that my litter was the problem, I figure lung problems means avoid dust). My was able to transition my cats to Yesterday's News, but it still has some dust, and I didn't like how difficult it is to remove urine-soaked yesterday's news. (It's much easier with a sifting box, but I didn't go that route.) I switched my cats to the Breeze Litter System, which is completely dust free. There is one huge thread on it here, but to put it simply, the breeze is inert pellets on top of a grid and a urine pad under a grid. You change the urine pad in the neighborhood of once a week, and the pellets much less often.
I love the Breeze: no more dust, no more tracking litter (the four stray pellets per cat per day are actually starting to annoy me, but I must simply remind myself of the alternative and annoyance evaporates), no more lugging heaving litter home.
Of course, neither the Breeze nor Yesterday's News is clumping, but that doesn't matter with the Breeze.