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I have a Colt 6920 as well. I have Timney trigger on it (4.5 lb), which was the first upgrade. I later added a Troy "D" rail to free float and to be able to add doodads to it (I really like the Troy rail and it is easy to install). I can't tell you that free floating the barrel improved things a lot as I did not do enough testing before and after to know. I have a 4X ACOG on the rifle (old, tired eyes).

I load my own ammo and can easily get the rifle to shoot around 1 - 1 1/4 MOA with inexpensive, bulk quality components (55 grain bulk Hornady bullets, Military Surplus pull down powder that is supposed to be like H335 and Tula primers with mixed brass off of the ground at PSC). I did shoot some Lake City ammo out of it when I first got it and that ammo was not that accurate (2-3 MOA) but that may have been a function of my less than great shooting skills at the time (I have taken several rifle classes since). If you don't reload and want some factory ammo that is accurate, try the IMI 77 grain ammo (SG Ammo has the best price that I can find). I have not shot that ammo in the Colt AR yet (I only use the Colt for matches out to 300 yards) but have shot plenty of sub MOA groups with that ammo in a couple of other ARs. I would try that ammo before replacing the barrel or other parts if you like the rifle the way it is now and don't want to spend money on the hardware.

FWIW, the barrel on the Colt has somewhere around 9,000 rounds through it and I can't tell any degradation in accuracy yet.