Weed killer. Get yourself a tank sprayer - the 3PH ones are best, but pricey. I use a 25 gallon tank with an electric motor that works great - I just throw the tank in my FEL or put it in a wagon and pull it. It wasn't too expensive.
For when that won't work, the push-style weed eaters are OK, as long as you aren't on hills. Ditto for a heavy duty sickle bar mower or push brush cutter. I've tried them and wind up going back to a line trimmer (sometimes with a blade, but I almost always use heavy duty line). If it is too steep for my tractor, it is too steep to push something up and down the hill, even if it is self propelled. Dang thing always tries to slide downhill (go figure).
Lots and lots of weed killer (glysophate works real well).