Circuit designer - DC motor reversal circuit

I use a basic remote control and relay to power DC motors. I'm looking to use two remote controls, one for forward and one for reverse. I've been using transistors and resistors to protect the batteries from polarity reversal. When I use AA or 9V batteries, the transistors can handle the amperage - 500milliamps or so and the motors forward and reverse. When I use RC batteries - 7.4v or 11.1v at 3-5Amps, the RC motors won't run and the transistors are getting fried. I don't want to use relays. I don't want to use ICs.
I need help determining the NPN transistors or other? (Mosfet) and resistors (best resistance) and the schematic(part numbers, transistor number) to make the RC motors run with as much power as possible.