As posted above you only need two outputs per motor. The most common L298 board has a dual motor output and 4 lines of input. Any Arduino board will manage that, I regularly use them with the Leonardo. That would be: No custom made parts, Easy to program, Reliable. Is it cheap enough and small enough? Custom would be smaller and cheaper if you are making a lot.
Are you just turning the motor on at full speed, then off after a time? A microcontroller and driver seems like overkill for that.
The L293 can get pretty hot, I wouldn't totally believe what the datasheet says. Will it handle 6.5A?