Yeah the MOSFET can sustain 55A in certain conditions of temperature/heat disipation and continuous signal, but i wouldn't get that close to the limit in this application. Anyway, it's current handling capabilities are exceeeding by a large margin the necessary in this situation, and you should be more concerned by the limitations imposed by the wires and connectors (and even the PSU's 5V rail) rather than the transistor.
Referring to the idea you've proposed, first of all you'll need two power transistors, one for sourcing and one for sinking, with separate buffer circuits for each. The other problem is that a Darlington setup means a base-emitter voltage drop of at least 1.2V, wich is simply unacceptable cosidering your output voltage must have a minimum of 1.25V. You must use MOSFET transistors wich don't have such limitations, but a problem with the control circuit appears, as these need a high gate voltage to completely open.