I would build this totally outside of Lectora where you have complete control over everything and then add it in a web window. You can add a hidden true/false Lectora question on the same page and assign the drag and drop score to it’s question variable. Attached is a rudimentary example that I think does most of what you are looking to accomplish. Keep in mind that to run the published material you need to be on a server (WAMP or XAMPP works too). You should be able to see it work in a Lectora preview too.
I know this is different from what the guys above suggest, which works as well. I commented the code a bit. If there is any interest, have questions or need help adding additional functionality let me know.