Nanostructures exposed to ultrashort waveform-controlled laser pulses enable the generation of enhanced and highly localized near fields with adjustable local electric field evolution. Here, we study dielectric SiO2 nanospheres (d = 100-700 nm) under strong carrier-envelope phase-controlled few-cycle laser pulses and perform a systematic theoretical analysis of the resulting near-field driven photoemission. In particular, we analyze the impacts of charge interaction and local field ellipticity on the near-field driven electron acceleration. Our semiclassical transport simulations predict strong quenching of the electron emission and enhanced electron energies due to the ionization induced space charge. Though single surface backscattering remains the main emission process for the considered parameter range, we find a substantial contribution of double rescattering that increases with sphere size and becomes dominant near the cutoff energy for the largest investigated spheres. The growing importance of the double recollision process is traced back to the increasing local field ellipticity via trajectory analysis and the corresponding initial to final state correlation. Finally, we compare the carrier-envelope phase-dependent emission of single and double recollision electrons and find that both exhibit a characteristic directional switching behavior.