Reconstructing a metric or vector potential that corresponds to a given solution to the Teukolsky equation is an important problem for self-force calculations. Traditional reconstruction algorithms do not work in the presence of sources, and they give rise to solutions in a radiation gauge. In the electromagnetic case, however, Dolan (2019) and Wardell and Kavanagh (2020) very recently showed how to reconstruct a vector potential in Lorenz gauge, which is more convenient for self-force. Their algorithm is based on a new Hertz-potential 2-form. In this talk, I will first show that the electromagnetic Teukolsky formalism takes a simplified form when expressed in terms of differential forms and the exterior calculus. This formalism makes the new Lorenz-gauge construction much more transparent, and it enables an extension to nonzero sources. In particular, I will derive a corrector term, related to the charge current, which when added to the vector potential gives a solution to the Maxwell equations with nonzero source. I will conclude by discussing prospects for extending to the gravitational case.