Your RC map looks to be correct. Get a AR 7700 receiver and use the PPM output into the Pixhawk RC in connection. Assuming you have a mode 2 transmitter all should be well I think. Steering should be on output 1 and throttle on output 3 on the Pixhawk to the best of my recollection. You will be using the right stick only for throttle and steering.
David R. Boulanger