In this follow up to our recent letter [F. Otto et al., Phys. Rev. Lett. 104, 027005 (2010)], we present a more detailed account of the superconducting transversal flux transformer effect (TFTE) in amorphous (a-)NbGe nanostructures in the regime of strong nonequilibrium in local vortex motion. Emphasis is put on the relation between the TFTE and local vortex dynamics, as the former turns out to be a reliable tool for determining the microscopic mechanisms behind the latter. By this method, a progression from electron heating at low temperatures T to the Larkin-Ovchinnikov effect close to the transition temperature T(c) is traced over a range 0.26 <= T/T(c) <= 0.95. This is represented by a number of relevant parameters such as the vortex transport entropy related to the Nernst-type effect at low T and a nonequilibrium magnetization enhancement close to T(c). At intermediate T, the Larkin-Ovchinnikov effect is at high currents modified by electron heating, which is clearly observed only in the TFTE.