hello again JC,
Still battering this old chesnut I see. If Kiteman cannot explain it to you and you cannot visualize what is happening by now, then god help us all.
To be fair however, I believe I do understand the point you are trying to make, and you are not completely wrong. (IMO).
By my own limited understanding, some points which may help clarify:
1) Neglecting any nuclear reactions for the time being, the only kinetic energy into the system, so far as any particles are concerned, is the 'impulse' imparted to the ions (/electrons) at initial injection into the system. This is in a (generally) radial direction.
2) The only potential energy in the system is established by the central (virtual) cathode (wrt injected ions).
3) The system can be considered as a harmonic oscillator, with a periodic exchange between potential energy and kinetic energy of any/each or the particles within it. What is 'tangential momentum' at one point in any particles trajectory about the system, becomes 'radial momentum' at pi/2 rads later in its orbit. Then vice versa. (Hence Kiteman's point on 1.5d dimensionality).
4) Most collisions in the system are considered 'elastic' or semi-elastic.
5) The main (only) loses from the system, are:
a) Bremsstrahlung (as you correctly state)
b) Particles (and their energy) lost/expelled from the system due to upscattering - in and around the core, and importantly from the outer edge region ('boiling off'/annealing). Particle loss is possibly the most important mechanism in mitigating the phenomenon you are trying to describe. (Although Brem may also become very significant at larger scale/energy levels).
6) Collision energies within the system are not 'rectified' in any way (as you correctly point out). (Though losses from the system are, by their very nature).
Thus, what I see, is an 'average' set of 'displacements' of 'ideal' elliptical orbits around the central core region (that is: statistically, many/most orbits will pass either side of the geometric centre of the device, by an amount related to the average 'thermalisation' (or net tangential component of velocity caused by collisions within the system).
This means that statistically I would expect an 'inner shell' of highest density, rather than a simple point centre.
Most importantly, is the aspect of average 'lifetime' of particles in the system. This is, by design, kept to be less than the overall critical thermalisation time of the system as a whole. (for the very reasons you (correctly) posit).
Polywell can only operate effectively within a very highly tuned regime. Outside of this, and as you say, the system becomes dominated by chaos.
Does this make sense to you?