Hey Rainy Day;
Don't know if this will work for your problem, but, when I was putting in my garden beds I knew that existing weed seeds would be a problem, so I dug the beds and wet them down with a lot of water then covered them with those clear plastic drop cloths. Here the sun is murder year round, but I did this in the summer and it did the trick! Who knows? Maybe this will work for you too.
