Doc B was posting at the same time, so some of the following is repeating his words in a slightly different way. Nevertheless, here are my comments:
There are two completely separate issues here:
1) As Doc B has said, but perhaps to clarify, a balanced cable has three wires (+. -. and Shield, sometimes called ground). A single ended cable has two (+ and ground). This leave a number of possible ways to interconnect with a cable. Balanced cables are wires with the Shield grounded at one end, or the other end, or both. The Shield may or may not be connected to the ground or the chassis or both, at one end or the other or both, in a SE-to-balanced connection. The Shield may be (at the balanced end) connected to the chassis shield, or the centertap (which may or may not exist). Each of these has different issues, so it is critical to determine how the cable is wired. Furthermore, a balanced input to the TVC might have the Shield connected to the chassis or the centertap of the transformer or to nothing at all. Again it is critical to determine how it is wired. I will further add that since two "identical" cables behave differently, they are not in fact identical.
2) The Reduction is optimal with a 50K load, but it can drive a load as low as 15K. 15K at 20Hz is 120 henries inductance. I can't find an inductance rating for the Promitheus TVC, so I can't usefully interpret the "10K impedance" specification - but if loss of deep bass is the source of "thinness" then a larger output capacitor will help. I would not go above 1.0uF because the distortion will increase and the gain will decrease, but that should take you below 10kOhms without other trouble.