A couple of things come to mind. I buy Glyphosate from the local feed store to spray things like this. An $18 quart of concentrate makes 40ish gallons, and lasts me a couple of years. I keep a band sprayed around trees, house, shop, fences, and keep a couple of drainage ditches under control with it. It really works great. I use a 5 gal backpack sprayer from Harbor Freight. 1 hour of spraying and you'd be done... Might need a touchup in a couple of months. Once the vegetation dies completely, it really doesn't look bad at all.
If killing it isn't the direction you want to go, you could rig up a redneck type of thing with a push mower. You said you have a tractor... I envision extending the lift arms with whatever (2x4's ?) about 6-8 feet and putting a push mower out there on it. Take the wheels off the mower and use the bolts to go through the 2x4s. Then you can raise/lower it down into the ditch with your 3pt lift. It wouldn't be perfectly manicured, but it's simple and cheap. A hoopty push mower from a Pawn shop would fit the bill. Whole thing for under $100. I bet it would work fine. Let us know!