As I interpret the datasheet the splash screen will automatically show up if the device does not receive the Auto-Baud character. Since you do not see the splash screen this means that the device did receive the Auto-Baud character. This means that the device would have sent an 'ACK' response back but your software is not recognizing that this has occurred.
I think that you should simplify your program and concentrate on getting this preliminary handshaking to work. I would do away with the serial monitor and use some LEDs for feedback. Perhaps a green LED for ACK and a red LED for NACK. Now you can use the hardware UART to communicate with your display, but make sure that you disconnect the display while you download your sketch. I would also try to simplify the serial communications as much as possible, perhaps by doing away with the arrays.
Remember that after the initial ACK (for the AutoBaud) the device does not respond until it has received what it perceives to be a complete command. If you send it a magic 0x42 it expects two more bytes. If you mistakenly send it three bytes it will respond after the second one (but you may not be looking for the response yet) and it will treat your third byte as the beginning of its next command. At this point you are waiting for an ACK and it is waiting for the rest of it's next command. I believe that the hardware serial may be better at sorting this type of problem out than the software serial.
Don