is right in the downwash of the rear wheel a good place to put an oil cooler? Any crap kicked up by the wheel is going to lodge between the pipes/fins if you're lucky. It'll get knocked to shit and busted if you're unlucky. How about forward of the wheels, like in the middle of the floor, ahead of the gearbox? Or above the A-arms/drive shaft beside the gearbox with a small scoop up to it? Just anywhere out of the debris shower from the wheels...
an in-line thermostatic valve would be a good idea too, to allow the engine to warm up properly and quickly before opening the circuit to the cooler. Like a water radiator in any non-air cooled car (*spit*)