I have some custom hardware that accesse the GM Single Wire CAN bus, this is the bus the BCM runs on. I'll see if I can find the codes necessary to auto enable competition mode.
Then I should be able to wire up a box to make it do it on start up that simply plugs into the OBD port
EDIT: I found the code the button sends out on the bus already, and isolated a start up code to base it off of. Wrote up a little script that monitored the codes for the trigger and then .5 seconds later sent the first push, and .5 seconds after that sent the next... Turned off the car and turned it back on and my car went into competition mode.