Accept the WL position now. Continue to update your application, and if you win any awards, improve your grades, etc., let them know. Lots of seniors slack off, so an upward trend now is your friend. ED applicants are appealing to take from the WL because they often agree to come.
In the meantime, you will need to accept a spot by 4/30 at another school. You will forfeit the deposit there if Tulane comes through, which you should not count on.
In a nutshell, you want to give Tulane a compelling reason to take you from the WL should an opening become available while embracing another school because the WL is beyond your control and may or may not move for you.