If you're eliminating Fate, I would take a serious look at Cortex Plus, as seen in the Cortex Plus Hacker's Guide. It's a modern game, powering a number of licensed properties, including Marvel, Smallville, and Firefly.
Taking your points, I think it satisfies most of them. Let's look at each:
role-playing is more important than combat (that is to say - the mechanics shouldn't encourage building the whole campaign around a large number of conflicts only)
In Cortex Plus, conflicts are conflicts. You can have an argument be just as important (and systematized) as a fistfight. And the system supports and encourages playing to a character's strength...and showing his weaknesses, too.
(tied to the above) I think it'd be great if munchkining / min-maxing wasn't possible or at least discouraged
I'm sure that it's possible to abuse the system, but Cortex Plus is emphatically not a game that's about builds. It's about characters.
we definitely want a system where the GM is the main storyteller - as such, Fate is a no go
I'm not sure what disqualifies Fate here, but Cortex Plus uses a standard GM - it's not GM-less like Fiasco or anything. That doesn't mean players don't get narrative power, they do. If you want players to have zero narrative agency, this is probably the wrong game for you. But I would examine the source of that desire, because narrative agency is fun...do you really need to hog it all?
the system shouldn't encourage potential fail scenarios for conflicts (example: failing in Fate doesn't mean characters die - it means things get more complicated. However, it seems my fellow players never really understand this and treat each conflict like a life-or-death situation, even if this was only subconsciously, leading to a lot of issues)
Cortex Plus is not deadly by default. Lose a fight in Leverage and you get get knocked out and maybe captured - out of action for a bit, but not dead. Same with Marvel.
no exploding dice
Nope. All non-explosive dice.
(preferably) normal distribution for die rolls
The basic Cortex mechanic is that the GM will roll 2 or more dice of varying sizes and select 2. The sum of those 2 becomes "the stakes", a value the player has to meet or exceed. The player builds a pool out of his applicable values and rolls, usually selecting 2 to sum. Various powers, distinctions, and point spends, etc., can change which dice are rolled and how many are kept. So while you're not rolling 3d6, like GURPS, the distribution for the pool will be normal.
no grids / figures / maps required
Cortex Plus fully supports the "theater of the mind" style of play it sounds like you prefer. I don't think there is a tactical, maps-and-minis option I have seen, even.