Obviously the biggest trump card against burn is Leyline of Sanctity. Drop that t0 of game 2 and they will have major problems. At the very least they'll waste a turn Wear // Tear-ing it and not doing damage.
Golgari Charm, imo, is a sideboard card.
I would probably play this like a BG rock deck as it is almost there anyway. 4 Abrupt Decay, 4 Maelstrom Pulse, maybe 4 Inquisition of Kozilek in the mainboard to go with Thoughseize. That's a crap ton of disruption that is sure to mess up anyone's gameplan.
+ 4 Inquisition of Kozilek
-4 Golgari Charm
-2 Putrid Leech
+ Lotleth Troll
-2 ...something, maybe land
+2 Maelstrom Pulse
SB - Sideboard is always meta specific. If you find specific cards better for your LGS, run them.
-4 Extirpate
+3 Surgical Extraction (I've rarely seen split second here be useful)
+3 Golgari Charm
-2 Putrefy (you already have plenty of disruption)
-1 Crime // Punishment (this seems like a solid card in this deck)
-1 Rain of Tears (Fulminator Mage would be better, but it's pricey. Hopefully the reprint brings it down a lot.)
+2 Leyline of Sanctity