Karl, you want something for total vegetation kill that has residual action. Roundup is not designed for residual action, only a one time kill, so it is not your best option.

Farm stores sell products for this use. Read the lables carefully, there are different options for mixing strength.

Personally, I use a product called Pramitol 25E on my farm. Mixed properly, it is good for 1 year or more. This is the same herbicide that many highway departments use to kill weeds along guardrails, etc. It is typically mixed with diesel, but it can also be mixed with water. A gallon of concentrate is good for 10,000 sq ft.