Non-coaxial 50 ohm cable for LVDS
I'm having a tough time finding higher gauge wire that specifies a characteristic impedance and I don't feel like putting two lengths of 100 ohm ethernet cable in parallel to make a single connection.


Cat  5 cable is 100 ohms differential, which is exactly what you want.

Your prototypical coaxial solution uses two 50-ohm cables for the two arms of a differential signal, giving 100 ohms differential. 

The twisted pair in Cat 5 gives the same differential characteristic impedance as the original solution.

Even if you used some different cable, for example with 85 ohms differential characteristic impedance, you could resolve the mismatch by changing the value of the termination resistor. 

Trying to combine multiple cables to change the effective characteristic impedance could only lead to pain and aggravation.

One difference: The Cat 5 cable won't shield the signal like coaxial does, but this is usually not a problem. Also, the Cat 5 won't provide any ground connection between the two systems, so you may need an additional conductor in your overall solution to connect the two grounds. If the link distance is very long you might also need to connect to the cable through a transformer at one or the other end to avoid common mode currents due to ground potential differences between the transmitting and receiving circuits.