A couple of things I would consider in your build. Take a look at Faxon Barrels. Specifically, their lightweight/gunner barrels - well regarded and will probably cost you less than DD (around $175).
Also, you don't necessarily need a 14.5" barrel to have a good lightweight build - just my 2 cents. I recently made a lightweight build that came in under 6lbs w/ a 16" Faxon Gunner Barrel - couldn't be happier. Having a 16" will also save you from the associated legal issues of having a rifle under 16" and give you the option to switch out any compensator/flash hider in the future - or even a suppressor for that matter. Sift through the forums on here, there's plenty of talk & review of the Faxon barrels - overwhelmingly positive.
http://faxonfirearms.com/
Second, w/ regard to compensators and volume/decibel levels.... Any un-suppressed shot fired indoors w/o hearing protection is going to be dangerously/damagingly loud - regardless of compensator or A2 Flash Hider. The avg increase increase in volume of any compensator is approx 5-10 decibels. This is minimal in the overall scope of things. Any un-suppressed shot from your rifle is going to be 155+ decibels which is dangerous for hearing. So an A2 Birdcage vs BCM comp isn't going to substantially affect or change the noise produced.
However, there are better options out there for comp's than the BCM. Check out the Strike Industries J-Comp (about $30). It's about 1/3 to 1/2 the price and its been shown to reduce recoil better than the BCM. The differences in recoil reduction btwn comp's are minimal - but they exist. Here's a vid testing 35 diff compensators and flash hiders (Including both the BCM & J-Comp) - it's not definitive by any means, but it serves as a good baseline:
https://www.youtube.com/watch?v=3FD-Rou9-9A
I recently put a J-Comp on an SPR build and am very happy w/ it. Looks great imo as well. Good luck, and enjoy building your rifle. Cheers.