I cannot see anywhere on the recipe page where I can submit it to the current contest.
Hey Summer of Eggplant,
When you are on the "My Recipes" page, click on the recipe you'd like to submit, then click "edit." Scroll down to the bottom and you have the option to submit the recipe to a contest.
You can do it from the Edit function - the option to submit to contest is near the bottom of the page once you open your recipe up.