Hello Jessica,
First, congratulations on your upcoming wedding! My husband and I honeymooned at Disney too...and loved it! You will too!
So the first spot I thought of for a great romantic burger is not truly "American" fare, but have you considered lunch at
Le Cellier in the Canada Pavilion in Epcot? The steakhouse has a great burger, and the menu will have enough choices for you as well.
If you choose the right quiet corner,
Liberty Tree Tavern has a bacon cheeseburger too.
Or you can head to Turf Club Bar and Grill at Saratoga Springs Resort. A bit out of the way but well worth it for the dark woodwork and great atmosphere. Plus the Surf and Turf burger is to die for!
I wish you and your Prince Charming many wonderful years together! Good luck on your pursuit for the perfect burger. And best wishes!