Kingmaker and Serpent's Skull might be to your liking. While they have opportunities for social situations and roleplaying, those aspects can be trivially ignored or minimized. Otherwise they are big sandboxes, where you can wander about and murder monsters to your heart's content.
Serpent's Skull as written, or a Rise of the Runelords where the GM is a little more forthcoming about where to go next (thus cutting out investigation & RP).
Council of Thieves books 3-5 are just a big string of dungeons (though books 1-2 certainly aren't).
But if you want the mother of all hack-n-slash, try Slumbering Tsar by Frog God Games.
Carrion Crown CAN be run as more hack-n-slash if you lead your players through the investigation and diplomacy aspects.
Kingmaker can also work, but the kingdom building aspect might be a little much for a novice gm.
Jade Regent has had a fair amount of combat thus far, but I haven't read the entire thing, as I'm playing in it. We've managed to get several combats into each session thus far, and, as far as subsystems go, the caravan has taken a small portion of overall table time. That might be the way to go.
Jade Regent has a steadily increasing RP part in the later modules.
Your best bet is to get several AP's and cobble together the big dungeons modules ( like Skeletons of Scarwall from Curse of the Crimson Throne and Shadows of Gallowspire from Carrion Crown ) into a new AP. :p
Curse of the crimson throne would be my suggestion - its relatively easy for npcs to send the party on missions, minimizing the investigative style (whilst still allowing players to take the initiative, if they feel like it). Having said that, pretty much all the APs can be played as combat heavy without too much effort, if that's your preference.