For those who have suggest just mowing with a zero turn must not have read the OP’s post fully. They have 5 MILES of fence line. Yes, on about a mile of our fence line I mow under the line and then come back and use my commercial grade line trimmer. Mowing a fence is slow going to be effective. You can’t just zip around like mowing a yard. 5 miles will take a considerable amount of time. And you will probably have to start all over again when you finish the last mile. Unless the season goes dry. Most of us who run large farms for a living don’t have a lot of free time unless we are lucky enough to have the income to support a full time maintenance crew.
Round Up would not be my choice for the same reason that others have said. Given a bit of time the grass will grow back. Why, because it is supposed to by design. Read the label it says to give X amount of time before replanting. Most grasses are spreading type through their root system. Which is why a weedy paddock will fill in with grass when board leaf weeds are killed off. Once Round Up has dissipated and the soil returns to it natural balance grass and or weeds will grow there. Ground clear is far more effective. But even that will dissipate given time. Ground Clear should only have to be used once a season where as Round Up will need several applications each season. Round Up was developed for commercial crop growing. It will kill off the weeds and other unwanted plants and then dissipate so farmers can plant their crop.
Diesel does work but it to does not last very long. Diesel kills by contaminating the soil with an oily film. The reason plants will grow back given time is Diesel is heavy and sinks, washes down into the soil. It has a very large soil contamination plume meaning it spreads as it sinks into the soil. Herbicides do not contaminate the soil to any where near the same extent. It kills off plants by being adsorbed into the plant and breaking down its cellular structure. Or something like that. It is basically a type of salt. It doesn’t smother the plant like Diesel. You don’t have to soak the soil with a herbicide.
I won’t get into a diatribe over the use of herbicides. I am good with how I feel about the judicious use of. Though I will over the use of Diesel.
As always to each their own. This is based on my experience in my neck of the woods. Believe what you want throw out what you don’t.