Killing Weeds Before Putting in a Raised Vegetable Bed?

I'm putting in a raised vegetable planting bed over a rocky area infested with invasive morning glory and large-form periwinkle roots. We have dug, pulled roots, and sifted the soil and after a 2 week period covered with tarps, found vigorous morning glory growth possibly from seeds. 1) How long does the plant killing action of vinegar last? 2) Will vinegar kill growth if it is under old carpet, then 18 inches of new topsoil? 3) Is there any other control method that works? Thank you for this?