Electron screening would seem to refer to the effect of the electron's negative charge neutralizing the positive charge of the nuclei, such that is allows two positively charged nuclei to approach with a minimal coulomb repulsive force.
Muonic hydrogen can penetrate the electron screen and catalyze fusion reactions. In the hydrogen molecule, the two protons are about one Bohr radius apart, 0.53 Angstroms. This distance is determined by the two electrons in orbit around the two protons, and is inversely proportional to the electron mass. If a heavy electron existed, the two protons would be a lot closer together. A negative muon, although it has a half life of about 2 microseconds, is about 205 times the mass of the electron and does form muonic hydrogen atoms. A muonic hydrogen (or deuterium) atom is very small and neutral (no charge), and will diffuse inside the electron screen (like a Trojan horse) and catalyze proton-deuterium (or deuterium-deuterium) reactions. I attach a bubble chamber picture of a muon stopping in liquid hydrogen (with some deuterium), and catalyzing two p-d fusions before decaying.