A take I'm surprised I haven't seen on the AS7-S yet on this board. Forget the energy hardpoints, just go for maximum instantaneous alpha. I get 71.5 firepower in this thing, and it's actually pretty heat efficient. Lots of ammo because once it's gone...it's gone.
This is a very well known build for the -S. It's indeed a surprise it hasn't been posted here, yet. You want as much speed (and twist speed!) you can get in this thing. The amount of ammo you are taking is VERY optimistic as you usually will get focused down quickly. Cutting some ammo allows to take a STD 350, though:
How does that compare with this? I've replaced the AC with a UAC, and got some more heatsinks, but at the cost of the Artemis accuracy. or you could even throw in a LB 20x and just forget about doing damage at range: At 9.31 sustained dps, you're going to be one fearsome brawler!
The LBX is an interesting choice. I don't like the UAC for this build because it isn't instantaneous in it's delivery. Keep in mind this build was made before IS had UAC20 or LBX20. Your builds skip Artemis, which I'd rather keep on 6s.
That's a lot of ammo for a brawler. I would upgrade to artemis and rebalance ammo (~30 LBX shots, ~22 SRM alpha strikes)