Our primary layout is 10,000 x 10,000 px, so #3 is definitely not true (it is not a single sprite though). As far as single image sprites, you might want to use a smaller image and use the tiled background?
I definitely think that some kind of tiled background is your best bet. You can always use other small sprites layered periodically on top to produce some variation in scenery, but the raw background needs to be tiled.