Do the job properly, using tinned copper is a very old unreliable technique, use the required copper on the board, with the correct weight of copper.
Use 2oz on the outer layers and you will gain extra when the board is plated up (talk to our manufacturer to see how much extra you will get)... Though 4oz is readily available.
Duplicate the power tracks on multiple layers.
Regarding PCB current, cause PCBs are designed to carry current, you just up the copper thickness, track width, duplicate the routes etc etc... We do boards that handle 60 A.