This is, as people have mentioned, not a great matchup for you. Karn Liberated in particular is pretty much going to sit there exiling things all willy-nilly. The artifacts, really, aren't what you need to worry about, so the counters you're running aren't going to be nearly as relevant. The only spells you're likely to counter at all would be All is Dust, Wurmcoil Engine, Mindslaver, and Karn Liberated (and possibly some of the SB cards), so save your counters for them. I wouldn't cut too many counters (remembering that you're going to be seeing Ancient Grudge, Seal of Primordium, Combust, and Pyroclasm second game), but you'll need some deck-specific hate after the first game.
Playing permanent destruction cards (Saltblast, Necrotic Sliver, etc.) and exiles (Extirpate, Surgical Extraction, etc.) get you the opportunity to take out their key lands. Some goofy things to deal with Tron include Herald of Leshrac and Helldozer, though I wouldn't say either are competitive enough for you to actually run. A third option and decent reanimation target (though fairly outside your mana base) is Realm Razer, though if he's already got some mana rocks out he's not as helpful.
Along with the permanent destruction strategies mentioned above, Scourglass can take care of Karn Liberated (and Emrakul, the Aeons Torn, but only for a little while). There's also Mangara of Corondor, which could make for a good reanimation target.
Stony Silence, while goofy, does seem like it would work surprisingly well - Mindslaver and all their mana rocks are dead in the water for CMC 2 sounds really nice. There's also Kataki, War's Wage - it could definitely slow them down a bit (and can be a reanimation target).
Aven Mindcensor does a particularly good job keeping them from using Eye of Ugin and Expedition Map properly, and makes your Ghost Quarters even better, so it seems like a prime reanimation target. Some alternatives include Leonin Arbiter, Mindlock Orb, and Shadow of Doubt (though Shadow doesn't have any real lasting power).
Unfortunately, Extract isn't Modern-legal. There is the idea of pre-Emrakul'ing them, though - something like Gather Specimens, Telemin Performance, or Bribery could work surprisingly well. You could also steal it by reanimating something like Conquering Manticore, Dominus of Fealty, or the new Zealous Conscripts (which could be interesting with Karn Liberated). Lastly, there's always Oblivion Ring and Journey to Nowhere, and Mangara of Corondor mentioned above could also work well.
Shimian Specter could actually be a very viable threat as a reanimation target here - if you can get him out and swinging, you can do some healthy damage to his deck. Yanking out those Urza lands (or if you're lucky, Emrakul, the Aeons Torn or Wurmcoil Engine) could be pretty rough for your opponent.
For everything I've already mentioned here, it still seems worth mentioning that only one Pithing Needle and two Mindbreak Traps seem a little low, and both of those cards seem like much better options than anything I've mentioned (except maybe Aven Mindcensor and Stony Silence). Needle Karn Liberated, and wait for a hard-cast Emrakul that you can trap it - they'll be running maybe four anti-artifact cards, so you running another Pithing Needle or two be smart. As for Mindbreak Traps, I'd say three might be the magic number, especially considering Snapcaster Mage.
Depending on what you can fit in, I'd say running Ghost Quarter and Aven Mindcensor or Stony Silence can also be a very good idea - play around with what feels best. Consider also that third game (if not second) you'll be seeing the Combusts and Pyroclasms, so that will cause some trouble for your Mindcensors.