My intention in this schematic is to throw the switch from K1.1 to K1.14 once the FET is set to 3.3V. In reality, once the device is powered, K1.6 reads 0.7V causing the switch to be thrown at startup, even if the FET's gate is at 0V. What am I missing?
Your schematic shows a p-channel mosfet while calling out an N-channel mosfet. A P-channel mosfet would give you exactly the situation you describe, with current flowing through the body diode to ground.
Verify you indeed do have a N-channel and the connections are correct.