While we're on the subject of patch bay features, I want to add that a good 1:1 line transformer like a Jensen JT-11SP-6M is a great thing to place behind the bay with points going in and out from the bay.
Since no wires actually touch(!) across the transformer, you can patch through it to break ground loops, eliminate DC offset, or interface "non standard" gear.
When interfacing balanced outputs and unbalanced inputs, it is often preferable to connect the cold (-) lead of the balanced output to the ground leg of the unbalanced input. This way, the signal that was on the cold lead is conserved in the input of the unbalanced gear, and the level remains consistent. Connecting the cold lead to ground on unbalanced inputs is so common, that many studios wire their unbalanced gear into their system this way, for seamless hookup with balanced gear.
Some transformerless but still "electrically" balanced gear, like my Apogee AD-8000, hates being connected out to an unbalanced input, (like an API 550B for instance), where the cold (-) lead has been shorted to ground on the unbalanced input in the manner I described above. The Apogee wants to see the cold lead left hanging, along with whatever level penalties that entails.
When one piece of gear won't play like the rest of the crew, you can't keep rewiring! One good answer is to simply use the patch bay and insert the line transformer between them. The transformer balances the input of the unbalanced device, so the interface mismatch is gone.
A solution to your unbalanced phase questions can be found here too...
Look: (ignore the periods, they are spacers)
UNBAL OUTPUT:.....(+)......(G)
into........................I........ I
XFRMR INPUT:.......(+).......(-)
xfrmer....................x........x
XFRMER OUTPUT:...(+)......(-)
into........................I.........I
UNBAL INPUT:........(G)......(+)......<-- Phase reversed!
The transformer creates a balanced signal at its output. The signal is in a push / pull (audio is AC current) configuration, so either side can be used as the (+) side, since both sides now have signal.
The reason is that since a transformer requires magnetic transfer for energy to move between its coils, all that gets across the transformer is any signal that can cause magnetism inside of it. Since magnetisim requires motion to create electricity, only the changing part of the signal (which makes the magentic field expand and collapse, which is equivelent to motion through a static field) will get across the coils in the transformer. Any DC offset that you may have picked up will be eliminated, since it has no changing component and will not create a CHANGE in the magnetic field, and therefore it will not create any electricity in the secondary coil.
This also means that while the signal going into the transformer may have been unbalanced - living on only one wire, with a ground reference on the other - that however the charge got into the coil is ultimately irrelevant. What gets across the coil, is the CHANGE, and since audio is Alternating Current, producing both negative and positive charges, the signal at the output is push / pull, with signal flowing one way, then the other. This is a balanced configuration, so the output of the transformer is always balanced. You could look at either leg of the transformer for the signal, it's just upside down on the cold (-) leg.
This is why you can selectively choose to connect either leg of a balanced output to the ground side of an unbalanced input, and still expect to find the signal on the other leg of the balanced output, and why you can reverse the phase of a signal after it has come out of a transformer without worrying about which leg has the signal. If you had done that directly with the unbalanced signal, you would have lost all the signal into the ground, and had nothing but ground into your (+) input.
Conversely, an UNbalanced output is not push / pull, and the information is only on one of the wires, referenced to ground on the other. You can connect it directly to any input, even a balanced one. No matter that all your signal is on one leg - the addition of the two legs (signal and nothing) will still yeild the complete signal.
To answer your application directly, I'd advise getting at least two transformers for your patch bay for stereo, and then making seperate phase crossing [(+) to (-), (-) to (+), and (G) to (G)] cords or PB points. That way, you can use the transformers and the phase flippers for seperate jobs when appropriate. Rememeber, those phase points and cords will work just fine without needing a transformer in balanced to balanced applications!
Good Luck!
Kyle