If you want a ragged hole at 100, ditch the .270 as I doubt it's going to happen on any kind of consistent basis. The BR guys will tell you "short and fat is where it's at". Not to say the long cartridges won't shoot, but a shorter and fatter powder column is more consistent and that's what you want.
But as far as a basis for an accurate rifle, you're not doing too bad. I have a Steven's actioned bench rig in .222 that will shoot .25" 5 shot groups pretty consistently. As far as changes made, I am running a SSS Dog Tracker stock, Timney trigger, Pac-Nor HV barrel, and have glass and pillar bedded the action to the stock.
If you want a ragged hole, you will need to spend some time and money to do it consistently. A stock with a flat fore-end is almost a must, though slightly rounded can work as well, but flat is better for tracking purposes and helps keep the rifle from torquing. You will need to improve the trigger, and a drop in such as the Rifle Basix SAV-2 will be fine. The factory barrel should go as well. They are usually far from the quality of a custom, and the .270 bore is more of a hunting caliber than a BR number. Look for something in the 6-6.5mm range with a HV or LV contour as the extra meat will help keep the barrel from overheating. There are a plethora of acceptable rounds for BR shooting.Though the short and fat rounds like the 6BR will recoil far less than larger rounds and are easy on barrels. Recoil will make handling a rifle on the bench much harder than a light recoiling round. They will pound you to death in short order. It's much more punishing than shooting in the standing position, as it is going to hammer straight back into you rather than push you back and allow the barrel to rise.
For a good, accurate, easy to load bench gun for 300yds, it's hard to look past the BR based rounds. The barrels will last a long time and recoil is basically nothing. If you really want to use the .270, it may be made to work, but will never keep up with a more efficient round. Efficiency is closely related to consistency, and you must be consistent to be accurate. The long powder column of the .270 doesn't lend itself to consistent ignition, as the flame has too far to travel. It also allows the powder to settle in different positions from round to round, as it almost always has a bit of empty space in the cartridge.
I have fired some larger rounds from bench guns, I have even screwed my .308 barrel on my bench rig just for fun and to see how it would do. The recoil made it much harder to control than my .222. I will take a small round like my .222 over a larger round any day of the week. Easier to control, and more fun from less work trying to control the rifle.
I too have back issues. Shooting anything over a .243 from a bench is uncomfortable for me. If you have had 5 surgeries, the .270 is going to be anything but fun.