balanced output VPI

I don't know the answer, but that is an interesting feature.

What does the manual say?

The Phono stage has only RCA inputs. There is a diagram in the manual describing how to wire an RCA interconnect to go from RCA phono box to the RCA input. As I interpret it:

The cable needs to have two wires and an external shield.

One wire is for the +ve (Middle pin), the other for the -ve (Barrel)
The shield is not terminated to the barrel.
The shield is terminated for both interconnects to the ground wire at the source end only. The ground wire to the junction box.

Imagine something like Belden 1800F, where instead of using XLR's you use RCA's.

Here is a link to vinyl engine that has a post on this:

http://www.vinylengine.com/turntable_forum/viewtopic.php?p=110009

To be honest though, I would probably just try it with a regular interconnect and see if it shows any promise.

No, you won't have to modify the box. Again, it's all in the manual.