This is what I did on my house. However it was when the house was being built and the foundation was exposed and not existing like you have apparently. I rented a plate compactor and compacted from the edge of the foundation out about 5 feet, sloping the dirt as shown in the image and the .pdf file. I never had issues with water in the crawl space.
It would be a challenge to dig up around the perimeter of your house and add drain pipe, etc. Maybe it would be better to address the flow of the seasonal stream and channel that?