Maintaining constant voltage at end of long wire
Given that you cannot use thicker wire or shorter wire, your options are: -

Boost the voltage at the sending end by a couple of volts and regulate down to the required voltage at the receiving end (more likely to work)
Boost and regulate the voltage both at the receiving end (might not work in extremes of load current due to cable resistance)
Boost somewhere in between and regulate at the receiving end.
Use a battery at the receiving end to supplement the load current required and let the battery be charged down the cable at a low average current (needs designing with care to ensure it works under all load/time scenarios).