The temperature, ac and dc field, and current dependent activation energy U(T,H)[(J(c0)/J(c))(mu)-1]/mu governing low-field flux creep in epitaxial c-axis-oriented HgBa2CaCu2O6+delta thin films has been determined from measurements of the frequency-dependent in-phase ac susceptibility. Above 35 K three different thermally activated flux creep regimes can be identified: (i) dislocation-mediated plastic flux creep, described by U(T,H) = U-0(1 - t(4))H-1/2 and mu = 0, (ii) elastic collective flux creep which decreases with temperature and has a weaker field dependence of H-0.22 above a field-dependent temperature Tc.(H) where A acquires finite values, and (iii) reappearance of dislocation-mediated plastic flux creep which rapidly increases as T-c is approached. It is argued that the re-entrant plastic-elastic-plastic vortex creep behavior is driven by the underlying temperature and field dependence of the shear modulus c(66). T-cm(H) marks a line in the H-T plane where the increasing c(66) promotes long-range correlations in the dilute vortex phase and creep becomes collective. At high H and T, c(66) again decreases and plastic creep reappears as the ordered phase starts to melt. Evidence for thermally assisted quantum creep is observed up to temperatures as high as T-0 = 35 K.