Recovery would be required of all stages, but re-usability not necessarily. Nothing coming in ballistic, but hard landing would be fine.I suspect the only way to design such a rocket would be for "recovery optional" of the lower stage or stages. If a heavy second/third stage sits on top of a 3-foot cardboard recovery section, I would expect that to be a likely failure point. The idea would be to keep this section of cardboard as short as possible. There are places where a rocket can be flown this way. If there's no rule about successful recovery of those sections, then the task is easier.
I also suspect that such a rocket would have to be minimum diameter. It is very difficult to fly non-minimum-diameter rockets to 100K, fiberglass or otherwise, due to the increased drag. I'm not sure it has ever been done? With minimum diameter, you have the motor tube to keep the air frame round. This is critical to keeping the fins on. I don't know about cardboard delamination, having never built a cardboard rocket, but I believe it might be possible to soak that portion of the air frame with epoxy to form essentially a composite structure with the cardboard. Again, if there's no rule ...
Active stabilization at the top of the rocket won't be practical. The weight of a system alone would be difficult to overcome. When I use active stabilization on high altitude flights, it is by locating the stabilization system between the first and second stages to "correct" the trajectory at that point in the flight. Then, that weight is discarded for the remainder of the flight. I've tried this three times on high altitude flights, and one time, it actually worked. Making this portion of the system out of cardboard would be pretty tough.
I do not agree on minimum diameter. If the velocity is kept low, drag is not as bad. I believe nobody has done non-minimum diameter, which makes this all the more interesting. It is worth noting that cardboard tubing is very lightweight and a careful structure might be possible. Also soaking cardboard to make a composite would be un-allowed. I know messy work is subjective, but I figure that is a good rule to have.
Do you have any documentation on your stabilization system? I think that is the hardest part. In previous posts myself and others outlined a way to do a series of air starts to achieve staging-like performance. One could combine that with your stabilization system. My initial thought is the booster would be long burning and need stabilization. The upper stage could be fin stabilized and "punch it" without much worry about aerodynamic stresses.