Okay I have done some research. Looking at webmaster mode, on the wishlist page, I see the array that holds the wishlist is assigned to this variable: {$wl_products} try searching through cart.php for variations of mode=wishlist and $wl_products. That should put you on the right track at least.
When mode=checkout, I don't think I saw this variable initialized in webmaster mode, but you should double check for yourself. Our task is to get this variable initialized and populated with the data when mode=checkout. Now at least we have a goal, and it has a name.
Let me know how far this gets you, and we will work further on it if necessary. BTW sounds like a cool mod you are doing, and a very creative way to use existing functionality! kudos.