The evolution of the electronic properties of electron-doped (Sr{1-x}La{x})2IrO4 is experimentally explored as the doping limit of La is approached. As electrons are introduced, the electronic ground state transitions from a spin-orbit Mott phase into an electronically phase separated state, where long-range magnetic order vanishes beyond x = 0.02 and charge transport remains percolative up to the limit of La substitution (x~0.06). In particular, the electronic ground state remains inhomogeneous even beyond the collapse of the parent state's long-range antiferromagnetic order, while persistent short-range magnetism survives up to the highest La-substitution levels. Furthermore, as electrons are doped into Sr2IrO4, we observe the appearance of a low temperature magnetic glass-like state intermediate to the complete suppression of antiferromagnetic order. Universalities and differences in the electron-doped phase diagrams of single layer and bilayer Ruddlesden-Popper strontium iridates are discussed. ; Comment: 12 pages, 12 figures. New version has revised text, added references, and updated figures