I have an 11.5 inch built with a Bushmaster heavy barrel. The best accuracy I can squeeze out of it with an acog at 100 yards is about 3 inches with handloads. I’ve tried several different ammo types and optics, and three inches is about the best it will do. Who makes an SBR barrel that I could expect MOA accuracy from?
HF
I would try LMT or Noveske.
Depends what you want to do.
Some of the BM barrels can be pretty good with the lighter 52gr bullets - a buddy of mine has one that can do near submoa with his 52gr VMAX loads.
However no factory barrels - be it Colt, LMT whatever is going to be able to guarantee a MOA - most will shoot near it, but not all.
If you want match performance will should look into a SS Match barrel
The wait for a 11.5 Noveske is about 16 weeks (as me how I know 
)
I’m not sure who else is turning SS SBR barrels currently
– I’ve had good luck with Douglas and Llija barrels done by CLE – but you’ll have to ask them if they will do a SBR for you.
My own personal feeling is to keep the BM barrel and play with the handloads – by and large if you have a SBR your not bench resting it - and the needs for a submoa/MOA barrel will be wasted by 99% of the shooters.
The wait for a 11.5 Noveske is about 16 weeks (as me how I know )
I didn’t know Noveske did 11.5" barrels. I thought it was 10.5, 14.5 or 12.5 well I guess I should check his site more often.
Well he will do any barrel you ask for – you just need to ask nicely and be patient.
Roger that.
Most chrome lined barrels out of ANY manufacturer is going to shoot between 2-4MOA. Sometimes you get lucky and get one that will shoot 1MOA.
If you want accuracy, you need to look at a SS barrel. Noveske makes some of the best IMHO.
C4
I am just starting to get into the AR thing…
I hope the 3-4 MOA is just for SBR
Barrel length has ZERO to do with accuracy. I typically build SBR’s that shoot half inch groups. It has everything to do with how the barrel was made and the chroming.
The acceptable MOA group size allowable (to the Military) is 4MOA @ 100yds. From what I have seen, most Civy AR’s with a chrome lined barrel shoot 2-3 MOA. There are occasions that you will get one that shoot’s 1MOA, but it is not common.
C4
You need to start getting Cold Hammer Forged barrels 
I’ve never seen a new Diemaco/Colt Canada barrel that could not hold 1MOA.
That said as far as Chromed barrels go I’ve seen a few dogs out there from other companies.
Heck, I would settle for just being able to get ANYTHING Colt. The SD chrome lined barrels seem to be a pretty consistant barrel (1-1.25) as well, but can’t get those either. 
C4
Frank @ CLE used to do short barrels so I assume that they still would. You can e-mail them at compasslake@earthlink.net and ask. But like Noveske, you have to ask nicely and be willing to wait a while.
And FWIW, the most accurate barrel that I have ever shot or owned was a Lilja that was done by CLE.
A SS Oly is the most accurate barrel I’ve ever used.