Wowsers - now that's taking a new approach for sure. I think even Varmint Al might have a tough time modeling the elastic behavior of that setup.
Here's something to ponder - the "stiff rod" in your diagram, what should it be made of? "Stiffness" is essentially Young's modulus (stress over strain). Individual carbon fibers are about 5 times stiffer than steel, with an atomic weight of 12, compared to iron, which has an atomic weight of 56-ish and a stiffness only 1/5th of carbon fibers. Check the technology of high-end bicycle frames (Tour de France type stuff) - they used to be made of steel, now they are virtually all carbon fiber. The stiffness of the CF can be controlled by the amount and directionality of the fibers, and the overall weight is a fraction of a steel frame.
I think there would be a benefit to making a "bloop tube" type tuner (or noodle) from a material with a very high modulus. (ideally, this would be either a ceramic composite or carbon fiber tube). By having a lightweight, stiff tube, the same moment can be applied to the end of the barrel with less mass applied to the end of the bloop tube. Hence, more "tuning effect" - (i.e. applied moment) can be had with less mass added to the end of the tuner.