Not sure it will help, but I've noticed that in the CCG4 EVK reference design and code they have changed so that you have only one VBUS_C/P_CTRL controlling two FETs, similar how you have have designed. I guess they did this change since there was not enough free pins on CCG4 since it controlls two USB-C ports. If you look into that design and the CCG3/CCG4 if-defs that exists in the code you might figure out how to reprogram the control logic as well. I might have opted for basing my design and code on the CCG4 instead?
Please kindly refer below comments for your concerns based on CCG3.
Is that possible with the CCG3 controller?
>> No. This is not possible with VBUS_C_CTRL_0/1. Since this two pins is controlled by hard IP block inside of CCG3. So that you cannot customize the firmware for this two pins.
It provides 4 driver outputs but can you control them separately?
>>If you could like to control this two path, you could have additional GPIO for additional one, otherwise this two paths will enable and disable same time when the Type-C port is attached and communication was done.
And do they have the ability to drive two FETs with ONE output?
>>For VBUS_CTRL is okay. If you are going to accept my suggestion on above, the normal GPIO cannot achieve this. Since you are using N MOS FET.