Our recent measurements (Lahmam-Bennani et al 2010 J. Phys. B: At. Mol. Opt. Phys. 43 105201) of the (e,3-1e) four-fold differential cross sections (4DCS) for double ionization (DI) of helium are extended here to a wider range of ejected electron energies and very asymmetric energy sharing. Previous observations of large angular shifts in the experimental 4DCS distributions with respect to the momentum transfer axis are once again reproduced by the new measured data. Moreover, a comparison of all the data sets with the kinematical analysis previously given and with two newly developed non-first-order theoretical models for DI-namely the two-step 2-Monte Carlo event generator (TS2-MCEG) and a second Born approximation (B2)-confirms our interpretation which allows the observed shifts and the existence of structures in the intensity distributions to be mostly related to the second order, TS2 DI mechanism, which is shown to predominate over the first-order 'shake-off' (SO) and 'two-step 1' (TS1) mechanisms under the present kinematics.