First problem. Its not AB til 4 stacks then barrage or missiles. Its keep your mana above 95% as much as possible.
On the pull. Prepot/Flame Orb, ABx3, PoM, AB, Mana Gem, Trinkets, AP, Images, then Burn to 30%. Evocate. Maintain mana above 95%. You may dip to 90% when things like power torrent or lightweave proc, that's ok. Use Flame Orb to proc arcane missiles to keep your mana up. When Mana Gem is off CD (NOT AP!) do your next burn, stacking as many CD's as possible (ABx3, PoM, AB, Gem, Trinkets, AP) and burn. Save your second pot for heroism (if it wasn't used on the pull) or for your third burn phase, when Images is off CD so that you get maximum benefit.
Staghelm is not a good fight, I'd look more at Baleroc. With all the leaping and runtime, I'd expect staghelm to be lower.