I’m trying to follow all of this and be helpful. I have a VPI table and unipivot arm, about which I have no complaints. But that’s not the issue. The issue is that your phonostage has balanced (XLR connector) inputs and the VPI signal block on the turntable has RCA connectors and a grounding screw. If your phonostage has a balanced circuit, then you are running balanced, even with all RCA connectors and two-conductor cables. Here’s why: at the phonostage end, the two conductors connected to the RCA termination are both "signal" leads and feed opposite phases of the input stage. At the turntable end, with the "box" the 2 signal leads of each RCA jack (which ultimately connect through the tonearm wiring to the signal lead pins of the cartridge) are not connected to ground. The ground connection is made by a wire that you install from the grounding screw on the VPI "box" to a grounding screw on your phonostage chassis. If you’re using a step up transformer (as I am), it also has a grounding screw (connected to the "cans" shielding the transformers), which needs to be wired by you to the grounding screw on the phonostage.
A so-called balanced interconnect, with XLR terminations, simply incorporates those 3 conductors into one cable and one termination: two signal conductors and a ground conductor. Cardas (and probably others) make an RCA to XLR cable that solves your problem. The XLR connectors on the cable go to the phonostage and, at the turntable end, the ground conductor in the cable is broken out so that you can connect it to the grounding screw on the VPI box. The two signal leads in the cable are connected to the two elements of the RCA termination. With this cable, you don’t need to have a separate ground wire between the phonostage and the VPI box on the turntable, because the ground wire is part of RCA > XLR cable. (And I'm not talking here about RCA>XLR "adapters," which are an entirely different animal and do not maintain the ground connection.)
In most arms, including the VPI arm, the 4 signal leads are electrically isolated from the arm or any other metal parts. So, this is a completely righteous setup . . . and you’re running balanced, whether you use two-conductor cables with RCAs or 3-conductor cables with XLRs at one end and RCAs plus a grounding wire at the other. Be aware, however that some moving magnet cartridges will couple one of the cartridge signal leads to either the cartridge body (if it’s metal) and/or the metal parts of the tone arm. This raises all kind of hell with ground loops, buzzes and hums. My first cartridge in this setup was a Clearaudio moving magnet that did this, and it took me months (and some expert assistance) to figure out the problem. The solution was insulating the cartridge body from the metal headshell and using nylon hardware to attach the cartridge to the headshell.
But you don’t need a new "box," you simply need 2 new cables. And, since you have to have cables between the turntable and the phonostage anyway, this should be a much cheaper solution than getting or modifying the VPI to make the connections I've described internally, rather than externally, which is standard.