Actually, your idea sounds perfect and you'd get a really good workout out of it! I'm not sure how anyone else does it, me, I just suck it up and use the band at its farthest ends I can reach while leaving a slight tension in the middle.
You might be able to stretch it like they do leather boots. Put the middle around something solid and stretch it out at both ends and tie it around another solid object that won't move (or fall!) and leave it for a while. Not sure how long to leave it, but you could check on it every 15 minutes or so.