I have similar ditches on my 0.6mi gravel driveway. While a seated-on-tractor solution would be plush... I can't find a viable solution at a reasonable cost.
I just walk with my high powered backpack blower and the hike up the driveway gets all the leaves and sticks out of the ditch and halfway across gravel. And then the return walk back down the driveway blows at all over into the woods on the other side.
I have to do this 3-4 times after the leaves fall to prevent the leaves and sticks from forming dams that divert the deluge of water runoff out into the gravel driveway where it erodes gullies. Its a situation where the ounce of prevention is definitely worth the pound of cure.