Sorry to be negative, but I wouldn't be putting down stone if it's that wet, you really wanted to have done the job when it was drier and compacted it down properly. Then, like others have said, strip off the top soil, make sure it can drain, lay down a good layer of type 1 or similar and compact (borrow a wacker plate). You might have to put some heavier stone underneath the type 1 depending on the conditions. I'm not a big fan of road planings, you need fines to bind stone together and in my experience planings doesn't have the right mix. It looks great for 5 minutes but doesn't hold together for long.