The 4H is the only QKD I kept, but it's still a mistery for me. Using all of the missile hardpoints and mounting bigger engergy weapons leads to very warm builds, but which I dislike. The loadout I settled on is an XL version of the old *Big Zombie* idea floating around when the QKD was new. It's pretty similar to your build. Your version is faster, but mine packs a little more punch. Although I mastered the mech, I am still not a strong believer in the chassis. Additionally I think it will become obsolete quickly with the jumpcapable 55t mechs as well as some kinde of improved weight class matchmaking on the horizon. In hindsight I probably should have kept the 5K, but who knows these things beforehand?
Personally I don't need a ton of speed in this thing, so I go in for about a 250 STD Engine. If you want to go in for a XL Engine however, this might suit your fancy. Granted the thing runs a lot hotter than the usual builds I see for brawlers, but I feel the Quickdraw can make use of its large frame to absorb damage while it cools off. That should get three missile bursts in junction with the lasers, but if you still want more efficiency, I'd recommend getting rid of the AMS and half a ton of armor for the extra heat sinks. The speed will help to get away from unfavorable LRM situations anyway.