I really must get George Burns. I do love thorns. Oh, and I think that was an AT&T jingle--could be wrong, that's just what popped into my mind when I first read it.
Perhaps you could pound in some green bamboo stakes (3 or 4) in close to the plant (about 2' off center maybe) and run some jute around and through the canes. Not so much that you would notice, but enough to keep the canes from swinging so freely. I'm not sure how tall or wide GB gets. The stakes don't need to go higher that the rose. I have seen this done. It doesn't look as bad as I am making it sound.