I suggest starting with this, if you haven't already: http://www.headphone.com/learning-center/balanced-drive-faq.php
The ideal way to form an all-balanced system is with: (1) balanced source component, (2) balanced amp, and (3) balanced headphones. There are caveats on each item though:
Balanced source component: These can be identified through their XLR outputs, which is standard for all balanced sources. However, not all sources with XLR outputs are necesarily "truly balanced". In order for a source to be balanced, it has to have what's called a "dual-differential DAC configuration", which essentially means there needs to be at least one, stereo physical DAC (chip) in each channel. Some DACs are mono-channel, which means that each channel will need 2 of that DAC, for a total of 4 in the source component - at least. Adding more DACs per channel lowers noise and offers other technical improvements, but manufacturers rarely do that, as it drives up cost.
A source with a dual-differential DAC config is where the entire system starts. If you don't have a source that meets this basic criteria, the whole headphone system will NOT be truly balanced. All of the sonic benefits from balanced operation won't be heard if this criteria isn't met.
I'd personally recommend not bothering with any balanced sources that cost less than $1K, because the inherent idea of balanced implies that it's two logical DACs, not just one, so it should be twice the price for twice the parts than a usual unbalanced source. In other words, a $1K balanced DAC probably won't sound any better than a $500 unbalanced DAC. To go a bit farther, I wouldn't personally waste any time & money on a balanced DAC that was less than $1.5K (excepting something made by Schiit Audio, maybe). And on a system for the SR-007, I'd increase that minimum to $3K, as the SR-007 is extremely revealing of the source component, much more than other headphones.
Balanced headphone amp: Some amps aren't truly balanced, and others are. An amp that's truly balanced can also be called a "dual mono" amp. Most traditional balanced amps are built this way and it's the ideal way to build a balanced amp, without clutter.
The amps that aren't truly balanced contain "phase inverters", aka "phase splitters", which can generate balanced output from only RCA input. The Woo WES sounds like it's one of these amps, from your description, when used via RCA input, anyway. (The amp would operate in solely balanced mode when using its XLR inputs, however.)
There are also other amps that generate balanced output through other means, without having XLR balanced inputs. While some of them do it legitimately, none of them will provide the sonic benefit that can be had through a balanced source.
Balanced headphones: Not all headphones necessarily support being able to be re-cabled for balanced drive. A certain number of wires have to be in the cable for it to work.
Also, not all headphones necessarily benefit from balanced operation either, and the most success will usually be realized on high-impedance/low-sensitivity or low-impedance/low-sensitivity headphones. I blanket recommend avoiding attempting to re-cable low-impedance/high-sensitivity headphones for balanced - every headphone I've heard of this type never benefitted sonically.
Note: this section doesn't apply for electrostatic headphones, as electrostatic amps are inherently balanced.
Balanced equipment: As I've gone through my own share of balanced sources, amps, & headphones, I'd flatly recommend against it in general. If you want to do it right, you have to be prepared to spend a lot of money, and potentially time. It takes a lot of effort to get a balanced system all in sync.
To achieve satisfaction faster and cheaper, it's easier to just stick with unbalanced equipment. I've found "balanced" to be vastly overrated and if I could go back in time, I'd choose the path of unbalanced gear instead.