From the looks of the targets your rifle/barrel is pretty much a 1 MOA rifle. I don't reckon that too bad for a feather weight barrel and that might be all your going to get out of the reloading components you're using.
I know IMR4064 has been a staple for the .308 Win for a long time. Not sure about the Bisley or what it is. I would try some more powders close to the range of IMR4064.
I had a stubborn .308 once, could not get it to shoot anything inside an inch and a half. It was a new factory barrel and I tried every powder I had and even bought a couple to try in it. Several different bullets and primer types later I decided to turn my attention to the rifle. I epoxy bedded the action and free floated the barrel, adjusted the trigger to 2lbs and that got it a little tighter, about a inch, but not what I had envisioned this heavy barreled, target rifle was supposed to do. I mean, come on, it's a dang .308. At this point I had spent close to a year troubleshooting this rifle.
In my searching the internet I came upon a gent who used a round headed, brass screw, valve grinding compound and a cordless drill to polish the crown. At first I was skeptical but then figured what the heck do I have to loose.
I polished the crown using the above mentioned items and wa-lah! the rifle thought it was a benchrest rifle! At 100yds it would put five in the same hole, or at least touching; using Varget, CCI BR2's and 175gn SMK's.
Sorry for being long winded but don't overlook the small things and don't be afraid to try something different. Good luck and let us know how it goes.
P.S. About a month after I finally got it shooting I pulled the barrel and installed a Shilen 6mmBR Norma. I still have the barrel and have considered putting it back on a couple of times.