The only things that affect the inherrent accuracy of an AR-15 are the barrel, barrel extension to receiver fit and ammo. There are other aspects which help the shooter make the shot more repeatable and thus increase practical accuracy.
If you put the best barrel into a sloppy receiver and torque it up, it is likely you will end up with shot drifting due to heat. I've seen plenty of ARs rebarreled with heavy barrels that won't shoot much better because the barrel extension to receiver fit is sloppy.
The best barrel for 3Gun is probably the Nordic 18" AR Competition barrel. I provided design specs to Nordic last year and they took the chance on it and had a bunch made. I've had customers shoot 1/2 MOA with the first group and all of the ones we have built will go under 1 MOA with quality ammo. It is what I use and I have not used a better barrel. It is the hot ticket!
Two ways to ensure barrel to receiver fit is tight: 1. Buy the barrel and go to the LGS and try receivers until you get the tightest fit. 2. Buy the receiver and barrel from a shop who will check fit fo you. Yes, the barrel extension can be externally coated with rockset and then torqued, but then you have lost the ability to change barrels.
Free float tubes are almost a necessity for 3Gun since the positions are so varied and contact will occur. The long tubes are what most competitors use with the carbon fiber tubes having a very solid following to keep the weight balance proper.
Play between the upper and lower reciever does not affect accuracy, but there is not reason to accept it either.
The stock is a shooter repeatability issue and it has to do with proper fit and head alignment with a quality optic.
In 3Gun, ALL barrels get hot. The mid-weight 18" barrels are the better balance of weight and accuracy. Only the pencil weight barrels will distort enough to affect accuracy. Heavy barrels add weight and therefore minimize poor technique, but they don't hold groups any better from a solid bench than a medium wieght barrel.
The better the trigger, the sloppier your technique can be. A CMC trigger or a Rock River 2 stage is about as good as you can get on the inexpensive side. From there, you can get up to $300, but for very little additional benefit. Trigger feel is subjective and there is no one best.
Hornady Steel Match or Black Hills reman match is as good as you can get and not go broke for ammo.
The one thing you missed is a comp. Some will carbon up in the high presure port and degrade accuarcy, but most will help you stay on target for the all important 2nd shot. A Nordic Corvette or Miculek is all you need. The Miculek is a tad easier to install and set-up whereas the Nordic can be tuned a tad more precisely.
Hope this helped.