I'm going to answer my own question, since I solved it with some additional poking around. Hopefully it will help someone else later down the road.
I didn't find a shortcode to to simply add the cart to the top of the checkout page. I had to edit the template file directly.
So, I copied:
/wp-content/plugins/woocommerce/templates/checkout/form-checkout.php
to:
/wp-content/mytheme/woocommerce/checkout/form-checkout.php
to make my edits to that file directly so I wouldn't lose them when WooCommerce was upgraded. I then copied the form code from:
/wp-content/plugins/woocommerce/templates/cart/cart.php
And pasted it in the file I copied to my theme directory:
/wp-content/mytheme/woocommerce/checkout/form-checkout.php
where I wanted the form to appear.
There may be more elegant ways, but this fixed my issue.