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In the first part of this series, we employed the second-order formalism andthe ``symbol'' map to construct a particle path-integral representation of theelectron propagator in a background electromagnetic field, suitable for openfermion-line calculations. Its main advantages are the avoidance of longproducts of Dirac matrices, and its ability to unify whole sets of Feynmandiagrams related by permutation of photon legs along the fermion lines. Weobtained a Bern-Kosower type master formula for the fermion propagator, dressedwith $N$ photons, in terms of the ``$N$-photon kernel,'' where this kernelappears also in ``subleading'' terms involving only $N$-$1$ of the $N$ photons.  In this sequel, we focus on the application of the formalism to thecalculation of on-shell amplitudes and cross sections. Universal formulas areobtained for the fully polarised matrix elements of the fermion propagatordressed with an arbitrary number of photons, as well as for the correspondingspin-averaged cross sections. A major simplification of the on-shell case isthat the subleading terms drop out, but we also pinpoint other, less obvioussimplifications.  We use integration by parts to achieve manifest transversality of theseamplitudes at the integrand level and exploit this property using the spinorhelicity technique. We give a simple proof of the vanishing of the matrixelement for ``all $+$'' photon helicities in the massless case, and find anovel relation between the scalar and spinor spin-averaged cross sections inthe massive case. Testing the formalism on the standard linear Comptonscattering process, we find that it reproduces the known results withremarkable efficiency. Further applications and generalisations are pointedout.

Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes