I'm out of ideas now, but John C. Reilly as O'Brien? They'd better chuck his Irishness if that was hypothetically the case, I don't want to see him (or any American actor, tbh) imitate the rather authentic average Irish guy persona that Meaney is so bleeding excellent at.
I agree, I can't see any non-Irish actors as O'Brien... For some reason, people keep nominating American and English actors for him (even posh, RP-accented, gorgeous English actors like Jack Davenport

unless that was a joke because his breakout role was of a bloke called Miles?). Reilly at least has the everyman thing down.
Nobody has yet nominated James Nesbitt for O'Brien?
Lots of good nominations above, quite a few of my favorite actors were mentioned (Andre Braugher, Christopher Eccleston, Lance Reddick, William Fichtner...). I like most of PSGarak's ideas - I didn't think of Asia Argento, probably because it has been ages since I've seen her in anything, but she may be a really good pick. Only I'd replace Ali Larter with Tricia Helfer. And I have no idea who Kal Penn is. I'm sticking with my initial pick for Bashir, even though he is not very well known - the only issue may be that I have no idea if he is is good in comedy, since I've seen him in just one thing, and it was such a dark role. But he would be really good in dramatic episodes, and it would be especially interesting to see him do darker stuff like Changeling Bashir, possessed Bashir, MU Bashir... I didn't get the idea just because the guy is a young, good-looking actor presumably of Arabic descent (even though not English but French) but because he was so convincing as an educated, charming, somewhat naive and impressionable young man who is at the same time so inscrutable that he can lead a double life and hide a terrible secret from everyone, including people closest to him. I think he'd convince me that Bashir had really been hiding the fact that he was genetically engineered all that time. Heck, he'd probably even make me worried for a moment if Bashir would really join Section 31!
But the role I really have the most problem coming up with ideas for is Quark. I don't think Rom is much of a problem, since all the actor has to do is act dumb/helpless and be somewhat likable nevertheless. So just find someone short who can do that. Willie Garson? Charles Martin Smith has to play a Ferengi, I'm just not sure which one.
Oh, uh, and Wayne Pygram as a Cardassian. Enabran Tain, perhaps.
Too young for Tain. But he could play some other Cardie.