The goal would be to transport a payload many times faster than a chemical rocket, and therefore go further in less time. For example, one might have a telescope orbiting somewhere out beyond Pluto. The goal of the Nuclear Pulse Autogyro would be to enable delivery/servicing/retrieval in a very short timeframe, weeks or months versus decades.

That's not to say it would actually work as well as hoped. There are alot of ideas out there and few have any significant hope of improving over conventional chemical rockets. The "hard analysis" that I have not done would be difficult. The AutoGyro is a periodically-forced 3-dimensional oscillating system, and my university dynamics courses are barely adequate. What is intuitively clear is that some force can be applied to a spinning rotor, and there will be some deflection.

Helicopters do this all the time: lift generated by the blades causes the blades to bend upwards, while centrifugal force opposes this by forcing them to remain largely horizontal. The result are helicopter blades spinning with a certain inclined angle relative to the flat plane (ground) that the helicopter is resting on, or flying over.

Another example is a string with a weight on the end. You can hold onto one end of the string and whirl it over your head. The force of gravity will pull down on the weight, while centrifugal force will try to make the string horizontal. The equilibrium state is that there is some angle of the string relative to the ground. You can whirl it pretty fast and the string won't break, and gravity is equivalent to a downward thrust on the weight. That's 1-gee of gravitational force PLUS the centrifugal force, and the string doesn't break. And yet, try to stand that string up on the ground and it will crumple under its own weight. A compression beam that would support the same forces would be much more massive than the string.

So the Nuclear Pulse AutoGyro should accommodate SOME force applied to the reaction balls. The question is, how much? And is the final system any less massive (cheaper to launch) than a simple Orion pusher plate would be?

So it would work, but I can't say how well it would work (yet). I really wish I had the time to work on it. Starship design is a long-time interest of mine.