A hand waving estimate can come from using the so called wave-particle duality ,
The deBroglie wavelength gives "dimensions" to scattering particles, useful for experimental estimates, without having to go through the scattering formalism.
in the equivalent form it can include photons:
The wavelengths give an estimate in classical terms of the size needed in focusing of the two beams so that the probability of scattering would be high. Scattering theory is used on the data to get the interaction crossection.
The real construction of the interaction region is a complicated process.
If two particles like these interact, is there any restriction on where the two photons propagate from [i.e. the same point, or just anywhere in the overlap etc]?
There is a definite mathematical system for calculating interactions of elementary particles , it is called quantum field theory,( quantum electrodynamics) for your interaction) and the calculations are done using Feynman diagrams to calculate the crossection in a perturbative expansion. The first order diagrams of e+e- to γγ (page 16)e_e-gamma
In the standard model of particle physics the interactions of the point particles happen at points called vertices , the impulse carrier is called a virtual particle, in this case a virtual electron. In the diagram time is in the y direction, and space the x. The photons appear at separate vertices. As it is functions under an integral in the x direction, it is not possible to define a unique distance or duration.
The Heisenberg uncertainty principle for the interaction will give a ΔpΔx region whence the photons may come.