It sounds like you want to use the USB Type-C connector for totally proprietary interface, and take advantage of having quality-built standard full-featured USB cables. Sounds reasonable to me. But since the cable doesn't have a key and can be plugged in both ways on both ends of your interface, you have to be smart how to use the wires.
The choice for your power "V" and ground is obvious - VBUS and GND.
Then, since you don't know how a particular cable is constructed inside for SS links (either 8 micro-coax or 4 twisted pairs), you should use them in "pseudo-differential" way, say connect your analog ground to Tx1-, and the signal to Tx1+. Same for SCL and SDA. For symmetry I would use D+ and D- for analog signal (it will be double shielded), and use Tx1(+,-) and Rx1(+,-) for I2C signals.
Now it is up to you to make parallel (cross) connections on your microcontroller (receptacle) side and sensor receptacle side, so that the cable orientation won't matter in all four variants.