Get a superlight barrel. Bushy or COlt is fine.
I have a 6520 and it's great. In my opinion, there is no need whatsoever for an HBAR, hell, no need for an M4 either unless you plan on getting a grenade launcher.
Yes, they will heat up faster, but they will also cool faster.
Superlight and Pencil are names given to these barrels since the market is dominated by civilian commercial HBAR's. Superlight and Pencil's are the REAL profile for an AR-15 rifle. The thicker barrel diameter forward of the FSB was made that way to handle a bayonet better. On 16" rifles, you can't fit a bayonet anyways. 14.5's are SBR's....so the only barrel that "needs" that is a 20". However, Govt profile 20"ers are light under the handguards.
Note that the lighter profile was designed and used for full auto or burst weapons. If the .gov thinks that's fine, it should be plenty fine for a semi-auto civilian rifle. If the military thought that they needed increased barrel mass to gain some sort of heat dampening propertied, they'd all be using HBAR's. The only heavy profile that I know of is the M4A1 barrel, and that is a special item because SEALS and what not are using their M4's as SAWs in massive SHTF gun battles doing mag dump after mag dump.
HBAR's are nothing more than a way for barrel makers to save on tooling wear and expense. Less time on a lathe, less metal to shave off.
Sorry for the rant. Get the "superlight" barrel. You will be glad you did. And when some tactical monkey at the range with his HBAR and massive rails and other crap mounted on there holds you rifle, they will remember that a carbine isn't suppose to weight 10lbs unloaded. Us superlight folks get criticized, but its our rifles everyone enjoys holding the most.