It is possible to make the inputs differential. Yes, one side needs 47k for proper impedance balancing (Ok, theoretically they should both be 23k, but it's not a big thing). Right now it goes to GND via 1 ohm resistor. The jacks are already lifted from GND. For other loading, just put a resistor across the inputs in parallel with the 47ks. Or you can put the 50 ohms right on the cart. No change to the 220 ohm grid stoppers necessary.
I doubt you will find any benefit. Best to use triaxial wiring. That is, twisted pair signal inside a grounded shield.
jh