"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?"

Well, it's pretty simple to know the most upper limit possible- the tensional strength of your cable.
For example
Elevator cable: 1/2" 14,500 lbs. per ft: .36 lbs $1.20
http://www.webriggingsupply.com/pages/catalog/wirerope_cable/elevator_wire.html

So, if one to use this elevator cable, one could not lift more than 29,000 lbs [each wire 14,500 lbs].
If you want 2 gees, than upper limit possible is 1/2 of this weight. 3 gees 1/3. 4 gees 1/4. Etc.

If you have say 5000' of this cable, the cable itself weighs: 5000 times .36 lbs = 1800 lbs

So, add whatever the weight of cable to the weight payload and then allow for whatever acceleration you are expecting.

Obviously you would need some kind of wire which better than elevator cable if you wanted much length of wire.

But then again why are we even using wire? Is the purpose to have some distance from the explosion? Won't the wire itself be exposed to this explosion?

If the wire would not be exposed to too much heat, then it's unlikely the spacecraft itself would be exposed to too much. Therefore what is reason the wire needs to be more than say 100' or say 500'?