My parents have a king. It sits on 2 twin box springs (we use the old ones from our childhood bedrooms; so they are indeed the actual size of twin beds). The only thing you would need to account for is if you delete the 2 borders in the middle (where 2 twin quilts would touch), you will need to add that amount back in somewhere. Adding an extra border could work -- that would make it a little bit longer, but that would probably look a bit nicer on a large king bed anyways.
Just make sure it is a true king & not a "California King". California Kings are a slightly different size.