I run the same cleaning procedures with my bolt rifles and get improved groups over the AR but the same consistency. My bolt rifles are in general factory rifles with custom barrels and I don't shoot the best grouping loads. I choose loads that are a compromise between group size and high velocity because the groups are close in size but the velocities are significantly faster, (up to 500 FPS) providing much flatter trajectory and wind drift due to reduced time of flight for varminting. The slower velocity can average 7/8" at 300 yards instead of 1 1/16" but the load just sucks in trajectory and wind drift over terraced farm fields.I don't know if you can improve the accuracy of an AR much by changing how you clean. They run a little differently than the bolt guns and match guns I usually shoot. The basic answer is if it is delivering accuracy you are happy with then stick with your current approach. If you want to tighten up groups then you'll have to experiment.
My LR BR rifles will shoot 1/2" groups and better at 300 yds in good conditions. The way I clean doesn't seem to make a huge difference, as long as I don't go too long between cleanings, get the barrel too dirty, speed it up, and put it out of tune.
It's always been my judgement that to improve the accuracy of these rifles I'd need to spend the time and money to improve the furniture bedding and machining of the action and barrel. I use moly and that improved the shot string count and has worked for decades over 2 barrels.