On the diagram, you show a rubber pad on the backplate -- presumably there to keep the nozzle /tail from getting damaged by bumping into the aluminum plate. (If this assumption is incorrect, you can probably ignore the rest of this post.)
I might suggest -- either along with or in place of the plate-bumper -- a stop on the launch rod designed to hold the plane away from the plate. Two possibilities that occur are:
1 -- a ring with a set-screw (so that you can adjust its position on the rod, then lock it into place) with a cushioning pad between the ring and the launch-glides, or;
2 -- a segment of the same tube used to line the launch-glides, sufficiently long to rest on the plate and to hold the tail of the rocket away from it, glued onto the rod.
Using a segment of the tube glued securely onto the rod -- but ONLY at the base near the backplate -- could have a secondary advantage: Since it appears to be reinforced with spirals of stiff filament or wire, then there should be some mechanical friction if the ends of two sections of tube should butt against each other, somewhat in the manner of lock-washers. This rotational friction between the ends of the buffer tube and the launch-guide tube, and the resistance of the reinforcing spiral fibers to uncoil may (I think!) serve to damp some of the swing of the plane on the launch-rod that seems to have so many commentators concerned. Attaching the buffer tube at the base, while leaving the end free to rotate slightly, then to "recoil" from the increased tension in the spiral filaments, should tend to resist the airplane's rotation and to push it back to a "neutral" position on the rod.