Single-particle spectroscopic probes, such as scanning tunnelling and angle-resolved photoemission spectroscopy (ARPES), have provided us with crucial insights into the complex electronic structure of the high-T-c cuprates, in particular for the under- and optimally-doped regimes where high-quality crystals suitable for surface-sensitive experiments are available. Conversely, the elementary excitations on the heavily overdoped side of the phase diagram remain largely unexplored. Important breakthroughs could come from the study of Tl2Ba2CuO6+delta (Tl2201), a structurally simple system whose doping level can be tuned from optimal to extreme overdoping by varying the oxygen content. Using a self-flux method and encapsulation, we have grown single crystals of Tl2201, which were then carefully annealed under controlled oxygen partial pressures. Their high quality and homogeneity are demonstrated by narrow rocking curves and superconducting transition widths. For higher dopings, the crystals are orthorhombic, a lattice distortion stabilized by O interstitials in the TlO layer. These crystals have enabled the first successful ARPES study of both normal and superconducting- state electronic structure in Tl2201, allowing a direct comparison with the Fermi surface from magnetoresistance and the gap from thermal conductivity experiments. This establishes Tl2201 as the first high-T-c cuprate for which a surface-sensitive single-particle spectroscopy and a comparable bulk transport technique have arrived at quantitative agreement on a major feature such as the normal state Fermi surface. The momentum dependence of the ARPES lineshape reveals, however, an unexpected phenomenology: in contrast to the case of under- and optimally-doped cuprates, quasiparticles are sharp near (pi, 0), the antinodal region where the gap is maximum, and broad at (pi/2, pi/2), the nodal region where the gap vanishes. This reversed quasiparticle anisotropy past optimal doping, and its relevance to scattering, many-body, and quantum-critical phenomena in the high-T-c cuprates, is discussed.