It would be better to add to your fat-quarter collection so you have enough fabric to make 1/4-inch seams.
As the other poster noted, close quilting will help reduce strain on the seams. However, with a king-size quilt there is still going to be a lot of stress on the pieced seams. Double-sewing will reinforce the seams somewhat, but it isn't a guarantee against fraying and it requires a lot of extra time.
Honestly, I'd just add more fabrics to the collection you already have. This will prevent problems with the quilt in the future.