Choose and assign questions (CPT) to quizes

I have created a special type of post (which is also a woo product), named Quizes (post_type = quiz). I also have another CPT, named Questions (post_type = question), which stores a multitude of questions and their multiple choice answers (the latter as their postmeta). As you can guess, the relationship between those two will be many-to-many, meaning that each quiz will have many questions, and each question can be assigned to many quizes...

Anyway, what I want is an idea of how to choose questions that would be assigned to each quiz. I'm looking for a method as practical as possible, and as close to a stock functionality as possible...

By practical I have categories assignment in my mind, where you have to check the ones your post belongs to, but when the categories are quite many (the questions will be MANY also), it's not so practical to choose among them in that small metabox on the right column of an edit page...

Also, I want the whole interface to be as stock looking as possible, so that I can re-use stock code instead of having to load external resource files... I.e, my mind went to the interface (I'm not sure if it has a name) where you have a list of possible options on a left column, and you drag'n'drop the desired ones to the right half column. This would be the most practical I can think of, but it'd require a lot of work to be done, and a lot of jQuery libraries to be loaded...

So I'm open to suggestions and ideas people. Thank you in advance! :)