But even slight lateral velocity will mean the ions miss this peak.
If that were a major problem, it would seem to preclude the formation of a double well, which we already have experimental proof of.
In particular, Ligon's notion that collisions out at the turn-around
point 'anneal' the distribution (never mind that getting one entropy-creating process to cancel out another entropy-creating process doesn't make sense thermodynamically) cannot then work, since collisions there will add angular momentum to the ion orbits, causing them to miss the central peak and take them out of the game
This point doesn't hold together very well. Entropy doesn't have to increase when the process of entropy increase itself adds the energy with which entropy can be reduced again. If you take a bunch of particles at low energy and apply energy to disorder them, they will naturally revert to their lower-energy, ordered state without addition energy input (picture nail filings in a magnetic field, or balls at the bottom of a valley).
By this argument, the Sun should fly apart, or be too diffuse for fusion due to angular momentum. Of course it doesn't and isn't, because the pull of the gravitational well is much more important than the disordering of the particle orbits. It's more a question of well depth (electrostatic or gravitic) than of fundamental workability.