Yes, you're right with compelling literature. I should've looked into the actual conditions the daughter joins are formed under but I typed it at 1am. I get rilled up if I see poor reasoning and tend to go after it without consideration of context and probably should've stopped after the first paragraph.

"Even [diatomic radical reactions] must fulfil strict geometrical (sic) conditions in order to pair lone electrons" I don't agree with. There is genuinely only 1 geometric paramater, i.e. the distance between the two atoms, unless you are implying Born-Oppenheimer doesn't apply or relativistic effects are necessary (which, they are, but for which your bouncing ball model doesn't account). Even the angle between their velocities does not matter following from Newtonian relativity.

I also believe your "energy threshold" (Eyering transition state Gibbs free energy?) is being imagined as far too high. Ground state monoatomic oxygen and lead must overcome only Pauli repulsion in the formation of the transition state, which will be on the same order of magnitude as Coulombic benefit entering the transition state, so I posit ca. 10% of bond enthalpy as the maximum barrier? Which for even the strongest diatomic leaves us with 90 kJ/mol, which for an ordinary reaction proceeds unmonitorably quickly at room temperature, for a more reasonable guess of 20 kJ/mol we need an argon matrix to observe these using IR spectroscopy. Reaction with triplet and heaven forbid singlet dioxygen will likely have larger barriers. Do I think these barriers will be large enough to stop reaction with a radon daughter lead? No not at all. Even under your assumptions.

Saying it will only occur when it forms larger clusters is frankly laughable. The ionisation energy goes up, the Gibbs free enegy of the transition state goes up, and frankly the chance of interacting with oxygen goes down, not up when forming a cluster. The total reactive lead surface area goes down rapidly with cluster size as core atoms become inaccessible, and on forming a cluster the volume goes down from overlapping atomic radii. On small clusters the cluster radius is a similar fraction of the mean free path as the atomic radius of a lead atom is of the mean free path, so forming a Pb(0) tetramer roughly quarters your reaction time. Lead metal sheets oxidises slowly, and can readily be chemically forced back to metal, however fine lead powder can ignite simply by throwing it through air.

Your assumption that lead clusters are forming in preference to reaction with oxygen is only true if your amount of parent radon is decaying much faster than it is diffusing or you have far more radon than oxygen. This is not true, as isolable radon (222Rn) has a half life of almost 4 days. Under any reasonable conditions this is much slower than diffusion and all radon will be well mixed with the surrounding air.

I would be frankly shocked to see any metallic lead deposition at all. I tried to read about experimental evidence for this however daughter isotope measurement is only performed by radiation measurments rather than any chemical means so the identity of the material is never stated (comprehensive article by Yamamoto et al. in J. Environ. Radioactivity).