Unfortunately this can't possibly work. The battery is basically shorted out on the bottom side of the motor.
The only way something like it could possibly work is if you get the other side of the motor to stay at half the battery voltage, without shorting it out. That's possible, but you'll only get half the motor's speed, and you'd have to either waste tons of power (wasting the battery really quickly) with a voltage divider, or make a more complicated circuit that's more complicated than getting a DPDT relay.
(noting that the diodes are actually the opposite way to how they're drawn in the picture) The diodes do not prevent current from flowing backwards to the battery. I don't understand what you mean by that. The diodes allow the current to flow in the same direction that it wants to flow anyway - i.e. from one side of the battery to the other - so they don't make any meaningful difference. If you turn either diode around it will block all the current and nothing at all will happen.