More thoughts from an armchair-rocket-engineer...
The article: "Battle continues over LOHAN's mighty rod" Published May of 2012, mentions something about a test launch of the rod system? Did that happen?
Below is a weight shedding scheme for the suggestion in my previous post but, first, for clarification of further discussion, my view of acceleration by a rocket:
1) In the initial portion of the launch the rocket's acceleration vector will be entirely determined by the relationship between the center of effort (CE) and the center of gravity (CG). This is the period where ground based rockets rely on a launch rod or rail. If the rod is not stable it will create wild asymmetry between CE and CG. Even a very small amount of friction at the rod-tube will (albeit briefly) mechanically couple the launch rig to the rocket - meaning their combined moment of inertia will determine the rocket's trajectory. Friction is a huge question mark; far too many parameters there for predictable/repeatable events.
2) In the second portion of the launch the direction of flight will be determined by the relationship between the rocket's CE and the center of aerodynamic resistance (CR). Ground based rockets have a thick atmosphere to work with, a lot of speed, and fancy vectored thrust to be able to enter this portion of the launch shortly after leaving the rod/rail. LOHAN does not - a variation from a ground based launch is a necessity.
3) This last portion aerodynamic stability, may never be attained (as has been previously discussed) due to the thin atmosphere and relatively small control surfaces - alas, I am not an aeronautical engineer specializing in high altitudes at mach speeds, so I can't answer that one!
Scheme for each of the above mentioned portions of launch:
1) Use a long weighted boom at the tail so that the rocket will literally stand on its motor. That is, if you supported the rocket at the nozzle does the entire aircraft point vertical? This is absolutely critical because of the lack of stabilizing rod and active stabilization.
2) Drop the weighted portion of the boom yet, leave enough boom length to keep the CR aft of the CE, which will be necessary for stable flight. perhaps as the rocket accelerates and the stabilizing effect of the rod increases, several potions of the boom may be dropped.
3) Drop the entire boom for aerodynamic flight, both during the burn and after.
Ahh, then the real trick right: Making it work.
Make the boom hollow with a long shaft running down the center. The shaft will be cut into portions coupled to each other with sockets. A servo rotates the shaft assembly which has several sets of unequal-length threads cut into each end. The first portion of the boom is bolted on by the shortest threads. The second portion and any subsequent portions have progressively longer sets of threads. Servo unscrews only enough threads to drop the intended portion.