It cost me $150 out of pocket to have it towed from Durant, Oklahoma to Joshua, Texas (thanks AAA). I did retrieve my spare. All the lugs were gone, of course. I considered your idea, but I couldn't get my bottle jack under the axle to lift it up and my farm jack, while handy in supporting recovery of other vehicles, is not tall enough to flex out the suspension enough to lift the rear axle on mine. I'm going to invest in a small and low profile floor jack just in case this sort of a thing happens in the future. It's something I've wanted in the truck for a long time, but never really justified needing.
This is an excellent idea. They come in a tidy plastic case and don't take up much room. SO MUCH easier to use than the factory jack and much more stable. I keep one in each vehicle I own. Spend the money for one of decent though. Though you'll not need it often, it needs to work when you do.
Something similar to this (not necessarily this one).