The DueX4 expansion pins that are available are listed at https://duet3d.com/wiki/Using_servos_and_controlling_unused_I/O_pins. What I can't remember is which ones (if any) are servo-capable. Any that are could drive the bltouch directly because it seems to be happy with a 3.3V signal.
Other than that, all of your suggestions sound suitable. For a level shifter, a small signal diode and pullup resistor to +5V would probably be sufficient.